Consider ABC.
What is the length of AC
A. 32units
B.48units
C.16units
D.24units
Answers
Segment GH is known as a mid segment, which is parallel and 1/2 of the segment parallel to it, in this case AC. :)
Related Questions
what’s is the distance between (-2,7) and (-5,9)
Answers
We can use the distance formula to find the distance between two points in a coordinate plane:
d = √[(x2 - x1)² + (y2 - y1)²]
where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
Using the given coordinates of the two points, we have:
x1 = -2, y1 = 7
x2 = -5, y2 = 9
Substituting these values into the distance formula, we get:
d = √[(-5 - (-2))² + (9 - 7)²]
d = √[(-3)² + 2²]
d = √(9 + 4)
d = √13
Therefore, the distance between the points (-2, 7) and (-5, 9) is approximately √13 units. We can also approximate this value as 3.61 units (rounded to two decimal places).
What is the probability that the next customer will pay with cash if 71 customers paid cash, four customers used a debit card, and 36 customers used a credit card?
Answers
The probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
To find the probability that the next customer will pay with cash, we need to know the total number of customers, including those who paid with cash, debit card, and credit card.
Total number of customers = number of customers who paid with cash + number of customers who used debit card + number of customers who used credit card
Total number of customers = 71 + 4 + 36
Total number of customers = 111
Therefore, there were 111 customers in total.
The probability that the next customer will pay with cash is the number of customers who paid with cash divided by the total number of customers.
Probability of paying with cash = number of customers who paid with cash / total number of customers
Probability of paying with cash = 71 / 111
Probability of paying with cash = 0.639 (rounded to three decimal places)
Therefore, the probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
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i need help with this
Answers
Answer:
[tex]x = \$2.06[/tex]
Step-by-step explanation:
Representing the price of one juice bottle as x, we can construct the equation:
[tex]15x + \$1.93 = \$32.83[/tex]
From here, we can solve for x.
↓ subtracting $1.93 from both sides
[tex]15x = \$32.83 - \$1.93[/tex]
[tex]15x = \$30.90[/tex]
↓ dividing both sides by 15
[tex]\boxed{x = \$2.06}[/tex]
Write and solve an inequality to represent the scenario, then explain the solution.
Brianna has a $50 online gift certificate from a book store. The cost of each book is $9. There is also a shipping charge of $5 for her entire order. How many
books can Brianna buy without spending more than her gift certificate amount?
Enter the correct answers in the boxes.
Answers
Brianna can buy up to 5 books without spending more than her gift certificate amount.
We can set up the inequality: 9x + 5 <= 50. where x is the number of books Brianna can buy. To solve for x, we can start by subtracting 5 from both sides of the inequality: 9x <= 45
Divide both sides by 9: x <= 5. The inequality 9x + 5 <= 50 represents the fact that the total cost of Brianna's order (the cost of the books plus the shipping charge) should not exceed the amount of her gift certificate, which is $50.
We subtracted 5 from both sides to isolate the term 9x and then divided by 9 to solve for x, which represents the number of books she can buy. The solution, x <= 5, indicates that Brianna can buy up to 5 books without going over her gift certificate amount.
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Solve the inequality -1/2x greater than or equal to 17. Graph the solution
Answers
To solve the inequality -1/2x ≥ 17, we can start by isolating x on one side of the inequality.
Multiplying both sides by -2 (and reversing the direction of the inequality since we are multiplying by a negative number), we get:
x ≤ -34
So the solution to the inequality is x ≤ -34.
To graph the solution, we can draw a number line and mark -34 on it. Then we shade all the values of x that are less than or equal to -34. This can be represented by a closed circle at -34 and a shaded line to the left of -34, indicating that any value of x in that range satisfies the inequality.
Here is a graph of the solution:
```
<=====(●)-----------------------
-34
```
The shaded part of the line represents the values of x that satisfy the inequality -1/2x ≥ 17, and the closed circle at -34 indicates that x can be equal to -34 (since the inequality is "greater than or equal to").
f(x)=x^2+6x+8
Rewrite the function into vertex form
Answers
y=(x+3)^2-1
have a good day :)
Answer: F(x) = (x + 3)^2 - 1
Step-by-step explanation:
Evaluate the line integral, where C is the given
curve.
C
y3ds,
C: x =
t3, y =
t, 0 ≤ t ≤ 5
Please provide the right answer.
Answers
Unfortunately, this integral doesn't have a simple closed-form solution. However, you can use numerical methods or software like Wolfram Alpha or a graphing calculator to approximate the value of the integral.
We have:
y = t and ds = sqrt(9t^4 + 1) dt
So, the line integral becomes:
∫C y^3 ds = ∫0^5 (t^3)(sqrt(9t^4 + 1)) dt
Using the substitution u = 9t^4 + 1, we get du/dt = 36t^3, which means dt = du/36t^3. Also, when t = 0, u = 1 and when t = 5, u = 1126.
Substituting these values and simplifying, we get:
∫C y^3 ds = (1/36) ∫1^1126 (u-1/4)(1/2) du
= (1/72) [(u-1)^2 u^(1/2)]_1^1126
= (1/72) [(1125)^2 (1126^(1/2)) - (1)^2 (1^(1/2))]
= 3555.89 (approx)
Therefore, the line integral is approximately equal to 3555.89.
To evaluate the line integral along the curve C with the given parameterization x = t^3 and y = t for 0 ≤ t ≤ 5, we need to find the integral of y^3ds. First, we need to find the derivative of the parameterization with respect to t:
dx/dt = 3t^2
dy/dt = 1
Now, we can find the differential arc length ds, which is given by the formula:
ds = √((dx/dt)^2 + (dy/dt)^2) dt
ds = √((3t^2)^2 + (1)^2) dt
ds = √(9t^4 + 1) dt
Next, substitute the parameterization of y in terms of t (y = t) into the integral:
∫(y^3 ds) = ∫(t^3 √(9t^4 + 1)) dt, with limits 0 to 5.
Now, evaluate the integral:
∫(t^3 √(9t^4 + 1)) dt from 0 to 5.
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GAMES- two friends are playing a game with a 20 sided dye that has all of the letters of the alphabet except Q U V X Y and Z. What is the probabilty that the dye will land on a vowel?
Answers
The probability of the die landing on a vowel is 1 in 5, or 20%.
In this game, the 20-sided die has the letters A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, R, S, T, and W. To calculate the probability of the die landing on a vowel, we need to identify the vowels present on the die and then determine the probability.
The vowels on this die are A, E, I, and O. There are 4 vowels out of the 20 possible outcomes, so the probability of landing on a vowel can be calculated by dividing the number of successful outcomes (vowels) by the total number of possible outcomes (20 sides).
Probability = (Number of Vowels) / (Total Sides)
Probability = 4 / 20
Now, simplify the fraction:
Probability = 1 / 5
The probability of the die landing on a vowel is 1 in 5, or 20%.
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Un medicamento tiene ciertos compuestos en las cantidades indicadas en la siguiente tabla:
Compuesto Cantidad en miligramos
A 0,6
B 0,402
C 0,08
D 0,46
Al ordenar la cantidad de compuesto que contiene dicho medicamento de menor a mayor, ¿Cuál es el orden correcto?
Answers
The correct order of the compounds in the medicine from least to greatest is: C, B, D, A.
To order the compounds in the medicine from least to greatest, we need to compare their amounts.
First, we can compare compounds A and C. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound C, which is only 0.08 milligrams. Therefore, we know that compound C is the smallest amount in the medicine.
Next, we can compare compounds B and D. Compound B has an amount of 0.402 milligrams, which is smaller than the amount of compound D, which is 0.46 milligrams. Therefore, we know that compound B is the second smallest amount in the medicine.
Finally, we can compare compounds A and D. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound D, which is only 0.46 milligrams. Therefore, we know that compound D is the third smallest amount in the medicine.
Therefore, the correct order of the compounds in the medicine from least to greatest is: C, B, D, A.
It's important to note that the amount of each compound in the medicine may have different effects on the patient's health, and that the order of the compounds from least to greatest may not necessarily reflect their importance or efficacy in treating a particular condition. The ordering of the compounds is simply a matter of comparing their relative amounts in the medicine.
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A national organization sets out to investigate the change in prevalence of HIV since the last census in 2010. A total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive. Assume that the data from the census indicated that the prevalence of HIV in the particular population was 7. 5%. A) Write out the null and alternative hypotheses for a formal test of significance. B) Interpret your results at 95% confidence
Answers
A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census
B) At a 95% confidence level, the critical value for a two-tailed test is ±1.96.
A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is still 7.5%. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is different from 7.5%.
B) To test the hypothesis, we can use a z-test for proportions. The test statistic can be calculated as:
z = (p - p0) / [tex]\sqrt{(p0(1-p0)/n)}[/tex]
where p is the sample proportion of HIV positive cases, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.
In this case, p = 468 / 4706 = 0.099, p0 = 0.075, and n = 4706. Plugging these values into the formula, we get:
z = (0.099 - 0.075) / [tex]\sqrt{0.075(1-0.075)/4706}[/tex] = 8.80
At a 95% confidence level, the critical value for a two-tailed test is ±1.96. Since the calculated z-value (8.80) is much larger than the critical value, we can reject the null hypothesis and conclude that there is strong evidence to suggest that the prevalence of HIV has changed since the last census. In other words, the prevalence of HIV is different from 7.5%.
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One angle of a triangle measures 10°. The other two angles are in a ratio of 4:13. What are the measures of those two angles?
Answers
Answer:
Step-by-step explanation:
Let's call the two angles in the ratio of 4:13 "x" and "y".
We know that the sum of all three angles in a triangle is always 180 degrees.
So, we can set up an equation:
10 + x + y = 180
We also know that x and y are in a ratio of 4:13, which means we can write:
x = 4k
y = 13k
where "k" is a constant that we need to find.
Substituting these expressions for x and y into the equation, we get:
10 + 4k + 13k = 180
17k = 170
k = 10
Now we can find the values of x and y:
x = 4k = 4(10) = 40
y = 13k = 13(10) = 130
Therefore, the measures of the two angles in the ratio of 4:13 are 40 degrees and 130 degrees, respectively.
Find, correct to six decimal places, the root of the equation cos(x) = x. SOLUTION We first rewrite the equation in standard form: cos(x) − x = 0. Therefore, we let f(x) = cos(x) − x. Then, f '(x) = , so Newton's method becomes xn+1 = xn − cos(xn) − xn −sin(xn) − 1 = xn + cos(xn) − xn sin(xn) + 1 . In order to guess a suitable value for x1, we sketch the graphs of y = cos(x) and y = x in the figure. It appears that they intersect at a point whose x-coordinate somewhat less than 1, so let's take x1 = 1 as a convenient first approximation. Then remembering to put our calculator in radian mode, we get the following. x2 ≈ 0.75036387 x3 ≈ 0.73911289 x4 ≈ 0.73908513 x5 ≈ 0.73908513 Since x4 and x5 agree to six decimal places (eight, in fact), we conclude that the root of the equation, correct to six decimal places, is .
Answers
Using Newton's method, the root of the equation cos(x) = x correct to six decimal places is approximately 0.739085.
To solve the equation cos(x) = x, we can use Newton's method, which involves repeatedly applying an iterative formula to approximate the root of the equation. We first rewrite the equation in the form f(x) = cos(x) - x = 0 and find its derivative f'(x) = -sin(x) - 1.
The iterative formula for Newton's method is given by xn+1 = xn - f(xn)/f'(xn). Applying this formula, we get xn+1 = xn + cos(xn) - xn sin(xn) + 1.
To start the iteration, we need to guess a suitable value for x1. From the graph of y = cos(x) and y = x, we can see that they intersect at a point whose x-coordinate is slightly less than 1. Therefore, we take x1 = 1 as a convenient first approximation.
Using a calculator in radian mode, we can apply the iterative formula to obtain the following approximations:
x2 ≈ 0.75036387
x3 ≈ 0.73911289
x4 ≈ 0.73908513
x5 ≈ 0.73908513
Since x4 and x5 agree to six decimal places, we can conclude that the root of the equation cos(x) = x correct to six decimal places is approximately 0.739085.
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La tangente de 60° es igual al triple de la tangente de 20°
Answers
The statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.
To solve the problem "La tangente de 60° es igual al triple de la tangente de 20°," follow these steps:
Step 1: Write down the equation based on the problem statement:
tan(60°) = 3 * tan(20°)
Step 2: Find the tangent values for the given angles:
tan(60°) = √3
tan(20°) = 0.36397 (approximate value)
Step 3: Plug the tangent values into the equation and check if the statement is true:
√3 = 3 * 0.36397
Step 4: Calculate the right side of the equation:
3 * 0.36397 = 1.09191 (approximate value)
Step 5: Compare the two values:
√3 ≈ 1.73205 (approximate value)
Since 1.73205 ≠ 1.09191, the statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.
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1. Solve the following set of equations by using substitution or elimination. (1 point)
[2x+y=1
2x+3y=-41
O (9,-18)
O (10,-19.5)
O (11,-21)
O (12,-22)
Answers
Answer:
C. (11,-21)
Step-by-step explanation:
Elimination
2x+y=1....(1)
2x+3y=-41....(2)
You can eliminate x in this case. (2)-(1)
2y=-42
y=-21.....(3)
You can substitute (3) in (1)
2x-21=1
2x-21+21=1+21
2x=22
x=11
Final answer: (11, -21)
This stop sign is a regular octagon. The length of one side is 8 inches and the length of the apothem is 9.65 inches. Find the area of the stop sign.
Answers
The area of the stop sign, given the length of one side and the apothem, would be 308. 8 square inches.
How to find the area ?To find the area of a regular octagon, we can use the formula:
Area = ( Perimeter × Apothem ) / 2
Initially, we must determine the perimeter of the octagon. Since it is a regular octagon all sides have an identical length. There are 8 sides with length equal to 8 inches; therefore the perimeter is:
= 8 x 8
= 64 inches
The area is;
Area = ( Perimeter × Apothem ) / 2
Area = ( 64 inches × 9.65 inches ) / 2
Area = 617. 6 square inches / 2
Area = 308.8 square inches
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A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is v(t) =1t^(1/2) + 4 Find the car's average velocity in (m/s) between t=4 and t=10.Â
Answers
To find the car's average velocity between t=4 and t=10, we need to use the formula:
average velocity = (change in displacement) / (change in time)
Since we are only given the velocity function, we need to first find the displacement function by integrating the velocity function:
displacement = ∫(1t^(1/2) + 4) dt
displacement = (2/3)t^(3/2) + 4t + C
where C is the constant of integration.
Since we are only interested in the change in displacement between t=4 and t=10, we can ignore the constant of integration.
change in displacement = [(2/3)10^(3/2) + 4(10)] - [(2/3)4^(3/2) + 4(4)]
change in displacement = 28.147 - 14.265
change in displacement = 13.882
Now we can use the formula for average velocity:
average velocity = (change in displacement) / (change in time)
average velocity = 13.882 / (10 - 4)
average velocity = 1.98 m/s
Therefore, the car's average velocity between t=4 and t=10 is 1.98 m/s.
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Shannon's net worth is $872. 17 and her liabilities are $15,997. If she pays off a credit card with a balance of $7,698, what is her new net worth?
Answers
Answer:
To calculate Shannon's new net worth after paying off her credit card, we need to subtract the credit card balance from her total liabilities, and then subtract the result from her net worth:
New liabilities = $15,997 - $7,698 = $8,299
New net worth = $872.17 - $8,299 = -$7,426.83
Based on these calculations, Shannon's new net worth would be -$7,426.83 after paying off her credit card. This indicates that her liabilities still exceed her assets, and she would need to continue working towards reducing her debt and increasing her net worth over time.
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Estimate to find the correct answer for each expression.
A. 270 349. 6 - 112. 8
B. 220 173. 3 + 78. 4
C. 240 817. 2 - 597. 1
D. 250 108. 8 + 159. 3
Answers
The correct answer of estimation for each expression is 269,900, 220,251.7, 240,220.1 and 250,268.1.
270,349.6 - 112.8 = 270,236.8
To estimate, we can round 270,349.6 to 270,000 and round 112.8 to 100. Subtracting 100 from 270,000 gives us 269,900. Therefore, the estimated answer is 269,900.
220,173.3 + 78.4 = 220,251.7
To estimate, we can round 220,173.3 to 220,000 and round 78.4 to 80. Adding 80 to 220,000 gives us 220,080. Therefore, the estimated answer is 220,080.
240,817.2 - 597.1 = 240,220.1
To estimate, we can round 240,817.2 to 240,000 and round 597.1 to 600. Subtracting 600 from 240,000 gives us 239,400. Therefore, the estimated answer is 239,400.
250,108.8 + 159.3 = 250,268.1
To estimate, we can round 250,108.8 to 250,000 and round 159.3 to 160. Adding 160 to 250,000 gives us 250,160. Therefore, the estimated answer is 250,160.
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Min wants to make 100 name tags with ribbons attached to them. Each name tag requires five centimeters of ribbon. She has 3. 25 meters of ribbon. Exactly how many more centimeters of ribbon does Mon still need to make 100 name tags?
Answers
Min still needs 175 centimeters of ribbon to make 100 name tags with ribbons attached to them.
To help Min with her name tags, we first need to determine the total amount of ribbon needed for 100 name tags. Each name tag requires 5 centimeters of ribbon, so for 100 name tags, we can calculate the total requirement as follows:
Total ribbon needed = (Number of name tags) x (Ribbon per name tag) = 100 x 5 = 500 centimeters
Min has 3.25 meters of ribbon, which we need to convert to centimeters to compare with the total requirement:
3.25 meters = 3.25 x 100 = 325 centimeters
Now, we can find out how many more centimeters of ribbon Min needs by subtracting the available ribbon from the total requirement:
Additional ribbon needed = Total ribbon needed - Available ribbon = 500 - 325 = 175 centimeters
So, Min still needs 175 centimeters of ribbon to make 100 name tags with ribbons attached to them.
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The sum of two integers is 21. The second integer is three more than the twice the first integer. Find both of the integers
Answers
Answer:
what integer?
Step-by-step explanation:
more detail please?
I NEED HELP FAST PLEASE!!!
A laptop computer is purchased for $1800. After each year, the resale value decreases by %30. What will the resale value be after 4 years?
Answers
Answer:
$432.18
Step-by-step explanation:
First year
$1800
- 540
$1260
Second year
$1260
- 378
$882
Third year
$882
- 264.60
$617.40
Fourth year
$617.40
-185.22
$432.18
Antonio and lizeth have a combined income of $83,366. they have 1099
forms which report $1,200 in interest. they also have $4,922 income from
rental property. they can reduce their income by $3,500. what is their
adjusted gross income?
Answers
Antonio and lizeth's adjusted gross income is $85,988.
To find their adjusted gross income, we need to start with their total income and subtract any adjustments.
Total income:
Combined income: $83,366
Interest income: $1,200
Rental income: $4,922
Total income before adjustments: $89,488
Adjustments:
Reduce income by $3,500
Adjusted gross income:
$89,488 - $3,500 = $85,988
Therefore, their adjusted gross income is $85,988.
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Tara tosses two coins. What is the conditional probability that she tosses two heads, given she has tossed one head already?
Answers
The conditional probability that she tosses two heads, given she has tossed one head already is: 1/3
How to solve conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
We are given that she has two coins.
She has tossed one head already
Let A be the event that two heads result and B the event that there is at least one head.
If S denote the sample space, then S={(H,H),(H,T)(T,H)(T,T)}
A={(H,H)}
B={(H,H),(H,T)(T,H)}
So, A∩B = {H,H}
P(B)= 3/4
P(A∩B)= 1/4
Hence P(A∣B) = P(A∩B)/P(B)
P(A∣B) = (1/4)/(3/4)
= 1/3
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At the Barilla plant in Ames, IA, a machine fills jars of marinara sauce with a population mean of 26. 2 ounces of sauce and a population standard deviation of 0. 04 ounces. To ensure the machine is operating properly, a quality assurance engineer randomly samples 34 jars out of all jars produced at the plant in the last week and finds the mean amount of sauce per jar is 26. 197 ounces. Select the correct description of the population in this study. Group of answer choices
Answers
The population in this study is the jars of marinara sauce produced at the Barilla plant in Ames, IA.
How can the population in this study be described?The population in this study refers to all jars of marinara sauce produced at the Barilla plant in Ames, IA in the last week. It represents the entire set of jars that the quality assurance engineer could potentially sample from.
The population mean is stated as 26.2 ounces, indicating the average amount of sauce per jar for the entire population. The population standard deviation is given as 0.04 ounces, representing the variability in the amount of sauce across all jars produced.
The quality assurance engineer randomly selected a sample of 34 jars from this population and found the mean amount of sauce per jar to be 26.197 ounces.
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Unit 6: similar triangles
homework 5: parallel lines & proportional parts
what are the answers to these equations? # 1-16
Answers
To understand how to approach problems involving similar triangles, parallel lines, and proportional parts.
When you have two similar triangles, their corresponding sides are proportional. This means that the ratio between the sides of one triangle is the same as the ratio between the sides of the other triangle.
If you have parallel lines cut by a transversal, corresponding angles will be congruent, which can help establish similarity between triangles.
For example, if you have two similar triangles ABC and DEF, where AB/DE = BC/EF = AC/DF, then you can use these ratios to solve for unknown side lengths or other values.
To answer questions 1-16, identify the given information and determine whether the triangles are similar. If they are, use the proportional relationships to solve for the unknowns.
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How do you solve these problems on Unit 6: similar triangles homework 5: parallel lines and proportional parts?
7. X-5/6 = 14/2x+3
16. X-7/35 = 4/x-3
Gabby had 578 yards of fabric. she used 3215 yards of fabric. estimate the amount of fabric gabby has left. 1 yard 2 yards 3 yards 4 yards
Answers
Gabby does not have any fabric left, as she used more fabric than she had to start with.
How much fabric does Gabby have left after using 3215 yards, and what is the estimate?
Based on the information given, Gabby started with 578 yards of fabric and used 3215 yards of fabric. To estimate the amount of fabric Gabby has left, we need to subtract the amount of fabric used from the starting amount of fabric:
578 yards - 3215 yards = -2637 yards
Since the result is a negative number, it doesn't make sense in this context. It's possible that there was a mistake in the numbers given, or Gabby used more fabric than she had to start with.
Without further information or clarification, we cannot estimate the amount of fabric Gabby has left.
To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount of fabric she had initially.
So, to find the estimate for the amount of fabric Gabby has left, we can perform the following calculation:
Estimate for the amount of fabric Gabby has left = 578 yards (initial amount) - 3215 yards (amount used)
Estimate for the amount of fabric Gabby has left = -2637 yards
However, the result is negative, which means that Gabby doesn't have any fabric left, and she needs to purchase an additional 2637 yards to make up for the shortfall.
Therefore, the estimate for the amount of fabric Gabby has left is 0 yards (she needs to purchase more fabric to continue her work).
Jackie planted 4 carrot plants per 5 tomato
plants. Match the coordinate pairs from the
table with the points on the graph.
Answers
Answer:
jackie has 4carrot and 5 tomato worth 25$
Someone help me please
Answers
The corresponding values for the triangle in the larger circle are;
1. Perimeter of Δ BSH = 71.4 cm
2. The measure of ∠SBH = 102°.
3. The area of Δ BSH = 41.54 cm²
4. The length of the circumference of circle B = 52.275 cm
How do you calculate the corresponding values for the triangle in the larger circle, like perimeter?1. The ratio of the perimeters of similar triangles is equal to the ratio of their corresponding sides. Since OB/OA = 4.25, we have:
Perimeter(Δ BSH) = Perimeter(Δ ARG) × 4.25
Perimeter(Δ BSH) = 16.8 cm × 4.25 = 71.4 cm
2. Since the triangles are similar, their corresponding angles are congruent. Therefore, ∠SBH = ∠RAG = 102°.
3. The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides. Since OB/OA = 4.25, we have:
Area(Δ BSH) = Area(Δ ARG) × (4.25)²
Area(Δ BSH) = 2.3 cm² × (4.25)² = 2.3 cm² × 18.0625 = 41.54 cm²
4. The ratio of the circumferences of similar circles is equal to the ratio of their radii or diameters. Since OB/OA = 4.25, we have:
Circumference(circle B) = Circumference(circle A) × 4.25
Circumference(circle B) = 12.3 cm × 4.25 = 52.275 cm
The above answers are in response to the following questions below;
Dante created the following measurements and calculations:
He then made the following measurements and calculations:
He calculated the ratio OB = 4.25.
OA
He measured the perimeter of Δ ARG, and found it to be 16.8 cm.
He measured ∠RAG = 102°.
He calculated the area of Δ ARG, and found it to be 2.3 cm2.
He calculated the circumference of circle A, and found it to be approximately 12.3 cm.
He would now like to calculate corresponding values for the triangle in the larger circle, and he needs your help.
Calculate the following, using your knowledge that all circles are similar, along with the data already collected by Noah..
5. Find the perimeter of Δ BSH.
6. Find the measure of ∠SBH.
7. Find the area of Δ BSH.
8. Find the length of the circumference of circle B.
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Lizzie's grandfather is investigating the interest-rate options of two college funds. Option A gives 3% annual interest compounded yearly. Option B gives 2% annual interest compounded quarterly. Lizzie's grandfather wants to deposit his money into an account for 16 years. He decides to invest $3000 in each account for 16 years. How much money will Lizzie have for college in 16 years, rounded to the nearest dollar?
Answers
After 16 years, compounded yearly, Lizzie will have $5,995.68 for college in Option A and $5,789.95 in Option B, rounded to the nearest dollar.
For Option A, the interest rate is 3% compounded yearly. Using the formula for compound interest, we have:
FV = PV x (1 + r)ⁿ
where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years. Plugging in the values, we get:
FV = $3000 x (1 + 0.03)¹⁶ = $5,995.68
For Option B, the interest rate is 2% compounded quarterly. We need to convert the annual interest rate to a quarterly rate by dividing it by 4. Then we use the formula:
FV = PV x (1 + r/n)^(n x t)
where r/n is the quarterly interest rate, n is the number of compounding periods per year, and t is the total number of years. Plugging in the values, we get:
FV = $3000 x (1 + 0.02/4)^(4 x 16) = $5,789.95
Therefore, Lizzie will have $5,995.68 for college in Option A and $5,789.95 in Option B, rounded to the nearest dollar.
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Which statement is the inverse of the following statement? If an isosceles triangle has a right angle, it has two 45 ∘ angles.
Answers
The inverse statement is "If an isosceles triangle does not have a right angle, it does not have two 45° angles."
The given statement is:
"If an isosceles triangle has a right angle, it has two 45° angles."
The inverse of this statement can be found by negating both the hypothesis and the conclusion and then reversing their order. The negation of the hypothesis is "An isosceles triangle does not have a right angle," and the negation of the conclusion is "It does not have two 45° angles."
Thus, the inverse statement is:
"If an isosceles triangle does not have a right angle, it does not have two 45° angles."
This statement asserts that if an isosceles triangle does not have a right angle, then it cannot have two 45° angles. In other words, if an isosceles triangle has only one 45° angle, it cannot have a right angle.
The inverse statement is logically equivalent to the original statement, and they are both true because they are both examples of the contrapositive of the conditional statement "If an isosceles triangle has two 45° angles, then it has a right angle."
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