The space available for a relay race at a carnival is 92.75 yards. A rules sign is placed 5 yards before the starting line. If there are 5 sections of th
start to finish and each section covers the same distance, how long is each section of the race?
Each section of the race is (blank) yards long
If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:
92.75 - 5 = 87.75 yards
Since there are 5 sections of the race, each section covers:
87.75 / 5 = 17.55 yards
Therefore, each section of the race is 17.55 yards long.
A lottery game contains 28 balls numbered 1
through 28. What is the probability of choosing
a ball numbered 29?
The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0
Probability: Calculating the probability of choosing a ballFrom the question, we are to calculate the probability of choosing a ball numbered 29
From the formula for probability
P(A) = Number of favorable outcomes to A / Total number of possible outcomes
From the given information,
"A lottery game contains 28 balls numbered 1 through 28"
This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.
Now,
We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,
Number of favorable outcomes = 0
Total number of possible outcomes = 28
Thus,
Probability of choosing a ball numbered 29 = 0/28
Probability of choosing a ball numbered 29 = 0
Hence,
Probability of choosing a ball numbered 29 is 0
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Which function does the dotted line represent explain how do you know
Answer:
Step-by-step explanation:
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
Find the missing variables. Write answer as
number. For example: If answer is 31° type
31
X=
□2°
xº
36°
y=
Z=
yᵒ
75%
78°
The values of missing variables are given by:
x = 51°, y = 105°, z = 90°.
We know that the sum of external and internal angles is 180°.
So from the given figure we can see that y° is the external angle and the corresponding internal angle is 75°.
So, 75° + y° = 180°
y° = 180° - 75° = 105°
And also external angle is right angle that is 90° and the corresponding internal angle is z°.
So, z° + 90° = 180°
z° = 180° - 90° = 90°
This is a pentagon and the sum of all internal angles = (5 - 2)180° = 3*180° = 540°
According to the given figure the sum of all internal angles of the pentagon is = (180° - 36°) + z° + (180° - x°) + (180° - 78°) + 75° = 144° + 90° + 180° - x + 102° + 75° = 591° - x.
So, 591° - x = 540°
x = 591° - 540° = 51°
Hence the value of missing variables are: x = 51°, y = 105°, z = 90°.
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Solve for x. Round to the nearest tenth, if necessary
Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:
tan ∅ = length of the opposite side / length of the adjacent side.
We are given the following information from the image above:
Reference angle (∅) = 43 degrees
length of the opposite side = x
length of the adjacent side = 2.8
Plug in the values:
tan 43 = x/2.8
2.8 * tan 43 = x
x = 2.6 [to the nearest tenth]
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Ruth has a cylindrical cup that is filled with water. The cup has a diameter of 2 inches and a height of 6 inches. Select the containers that could hold all of the water in Ruth's cup
Since the containers were not given in the question, In a case whereby Ruth has a cylindrical cup that is filled with water where the cup has a diameter of 2 inches and a height of 6 inches, the volume of cylinder cup is 18.85inch^3.
How can the volume be calculated?Note that ; the container were not given in the question, so we will just need to calculate the volume of the cylindrical cup to know how much water it can hold .
The volume of a cylinder can be caluculated using te exppresion π r² h
Then from the question the diameter = 2 inches radius = 2/2 = 1 inches
height =6 inches
π r² h
=π * 1^2 * 6
=18.85inch^3
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Can you help me rewrite this in other words?
Part a
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
2. The chi square equals 1947 with one degree of freedom and the p-value being a non-zero number.
3. Since the p-value is less than the significance level, which would be .05, we rejected null hypothesis that would show that there is a significant association between climate change and a certainty.
Part 2
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
2. The chi square was 119.864 with 12 different degrees of freedom the p value for this is also a non-zero number.
3. Since the p value is less than .05, we would reject to null hypothesis, which would make sense that there is a significant association between sleeping and income class.
The discussion for both cases is shown below.
Part a:
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.
The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.
Part 2:
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.
Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.
In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.
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For her geography project, Karen built a clay model of a
volcano in the shape of a cone. Her model has a diameter
of 12 inches and a height of 8 inches. Find the volume of
clay in her model to the nearest tenth. Use 3.14 for pi
Answer:
301.4 in^3
Step-by-step explanation:
Divide 12 by 2 to get the radius
12/2=6
Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.
6^2=36 36*3.14=113.04
We now have the area of the base.
Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.
113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.
Use the substitution u = 1/y and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. -3/x + 4/y = 5 and 1/x - 2/y = -3
combine like terms 6x^2 - 10x + 21x - 35 = 6x^2 + 11x - 35
Answer:
Step-by-step explanation:
6x² - 10x + 21x - 35 = 6x² + 11x - 35
6x² - 6x² + 11x - 11x - 35 + 35 = 0
0 = 0
The equation is an identity. Its solution set is {all real numbers}.
Complete part (a) and part (b) given the following system of equations. x+y=0 -3x+4y=14. Solve this system graphically.
Answer:
Step-by-step explanation:
[tex]\left \{ {{x+y=0} \atop {-3x+4y=14}} \right.[/tex] ⇔ [tex]\left \{ {{y=-x} \atop {y=\frac{3}{4} x+ \frac{7}{2} }} \right.[/tex]
Help pls i dont understand this
The percentage increase in the number of water bottles the company manufactured from February to April is 19%.
How to find the percentage increase ?In March, the company manufactured 7% more water bottles than in February:
Number of water bottles in March = 4,100 + 7% of 4,100
Number of water bottles in March = 4,387
In April, the company manufactured 500 more water bottles than in March:
Number of water bottles in April = 4,387 + 500
Number of water bottles in April = 4,887
To find the percent increase from February to April, we can use the following formula:
percent increase = (new value - old value) / old value x 100%
percent increase = (4,887 - 4,100) / 4,100 * 100%
percent increase = 787 / 4,100 x 100%
percent increase = 19%
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I need help with this please.
1/2 x 3 x 3 = 4.5
I just need help on how 4.5 is the answer.
Answer:
3
Step-by-step explanation:
3 * 3 = 6
1/2 * 6 = 3 not 4.5
Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.
The 3 x 3 part turns into 9
So we have 1/2 x 9 or 9/2
Use long division to find that 9/2 gives a quotient of 4 and remainder 1
Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.
The "remainder 1" then leads to 1/2 = 0.5
quotient = 4
remainder = 1 ---> decimal portion = 1/2 = 0.5
So that's how we get to 4+0.5 = 4.5
You can use a calculator to see that 9/2 = 4.5
Which function equation is represented by the graph?
ANSWER: f(x)=40(2.25)x
just took the test
40(2.25)ˣ function equation is represented by the graph transformation.
What do graph transformations mean?
Changes to the graph of a parent function are referred to as transformations. Transformations may be divided into three categories: translations, reflections, and dilations. There are two types of transformations that may be done to a function: vertical (which affects the y-values) and horizontal.
(affects the x-values). The following guidelines apply to the function translation and transformation: The function is moved up b units by f (x) + b. The function is moved downward by the notation f (x) b. The function is moved left by the value of f (x + b).
Let the function be of the form
f(X ) = a(b)ˣ
Then the point (0,40) lies on the graph of this function. This point must satisfy the equation of the function.
We substitute the point to get,
40 = a(b)⁰
This implies that,
40 = a(1)
40 = a
We substitute a=40 into the function equation to get,
f(x) = 40(b)ˣ
The point (1,90) also lies on the graph of the function. This gives us,
90 = 40(b)¹
90 = 40b
b = 90/40
b = 2.25
We substitute the value of b also into function to get,
f(X) = 40(2.25)ˣ
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A scientist has two solutions, which she has labeled solution a and solution
b. each contains salt. she knows that solution a is 65% salt and solution b is 80% salt. she wants to obtain 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
What is the least common dominator of 4/13 and 4/5?
Answer:
52 is the least common dominator
Answer:
52/65
Step-by-step explanation:
The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.
The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple
The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.
The simple method for common computing denominators (not least at all) is to multiply all denominators.
Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.
What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?
The measure of ∠ADC is equal to 180 degrees.
The measure of ∠ABC is equal to 90 degrees.
What is a circle?In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.
In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.
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Choose yes or no to tell whether the equation has the given solution 1/4×+3=3=4×+ 1,x=8
Answer:
[tex]\large\boxed{\tt No.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to determine if the equation has a solution given a value.}[/tex]
[tex]\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}[/tex]
[tex]\textsf{the equation.}[/tex]
[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]
[tex]\textsf{The Substitution Property of Equality is a Property that allows us to substitute}[/tex]
[tex]\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}[/tex]
[tex]\textsf{After Substitution, we can prove that the expressions are still equal with this}[/tex]
[tex]\textsf{property.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\tt \frac{1}{4} x + 3 = " 3 = " 4x+1[/tex]
[tex]\textsf{There's likely a typo in your equation given, hence I will fix it.}[/tex]
[tex]\tt \frac{1}{4} x + 3 = 4x+1[/tex]
[tex]\textsf{Substitute 8 for x in both sides of the equation using our property.}[/tex]
[tex]\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]
[tex]\tt \frac{1}{4} (8) + 3 = 4(8)+1[/tex]
[tex]\underline{\textsf{Follow PEMDAS, multiply first;}}[/tex]
[tex]\tt 2 + 3 = 32+1[/tex]
[tex]\underline{\textsf{Evaluate;}}[/tex]
[tex]\tt 5 \neq 33[/tex]
[tex]\textsf{If the "typo" was the actual equation;}[/tex]
[tex]\tt 5 \neq 3 \neq 33[/tex]
[tex]\large\boxed{\tt No.}[/tex]
Find the missing information for both parts below.
The unknown angles in the circle are as follows:
a. m∠AEB = 73°
b. arc angle VW = 155°
How to find arc angles in a circle?a.
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
m∠AEB = 1 / 2 (99 + 47)
m∠AEB = 146 / 2
m∠AEB = 73 degrees
b.
If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .
Therefore,'
arc angle VW = x
55 = 1 / 2 (x - 45)
55 = 0.5x - 22.5
0.5x = 55 + 22.5
0.5x = 77.5
divide both sides by 0.5
x = 77.5 / 0.5
x = 155 degrees
Therefore,
arc angle VW = 155 degrees
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For the following exercises, convert the angle measures to degrees.
9π/5 b) - π/3
(round to two decimal places)
a) The measure of 9π/5 radians in degrees is approximately 324 degrees.
b) The measure of -π/3 radians in degrees is approximately -60 degrees.
To convert the given angle measures from radians to degrees, we can use the formula:
angle in degrees = (angle in radians) × (180/π)
a) To convert 9π/5 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (9π/5) × (180/π) ≈ 324 degrees (rounded to two decimal places)
b) To convert -π/3 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (-π/3) × (180/π) ≈ -60 degrees (rounded to two decimal places)
In general, we can convert an angle measure from radians to degrees by multiplying it by 180/π. Since π is an irrational number, the conversion factor 180/π is an irrational number as well. Therefore, when we round the result to two decimal places, we are actually approximating the true value of the angle measure.
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you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm
The rectangular block of wax can make approximately 2 candles.
How do we determine the number of candles that could be made by that block of wax?To calculate the number of candles, we use the formula
V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm
V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm
1800 / 972 = 1.85
The above answer is based on the full question below;
you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.
The height of the candle is 12cm and the base width is 9cm
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PLEASE HELP PLEASE!!
Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
Answer:
√75 =8.66.
Step-by-step explanation:
The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8.660.√75 cannot be written in the form of p/q, hence it is an irrational number. irrational with never-ending digits.
How to Find the Square Root of 75?Let's see how to find the square root of 75 by the long division method.
Step 1: Express 75 as 75.000000. We take the number in pairs from the right. Take 75 as the dividend.
Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 75.
Step 3: Now double the quotient obtained in step 2. Here is 2 × 8 = 16. 160 becomes the new divisor.
Step 4: Apply decimal after quotient '8' and bring down two zeros. We have 1100 as the dividend now.
Step 5: We need to choose a number that while adding to 160 and multiplying the sum with the same number we get a number less than 1100. 160+ 6 = 166 and 166 × 6 = 996. Subtract 996 from 1100. We get 104
Step 6: Bring down two zeros again and place it after 104, so that it becomes 10400 which is the new dividend. Now multiply the number in the quotient by 2. Here it is 86. We get 172. Have it as 1720. Now find a number at the unit's place of 1720 multiplied by itself gives 10400 or less. We find that 1726 × 6 = = 10356. Find the remainder.
Step 7 : Repeat the process until we get the remainder equal to zero. The square root of 75 up to two places is obtained by the long division method. Thus √75 = 8.66
Category: nr percentages
question_id: 5782
Alex is really upset. He invested a lot of money in shares and only has $72,800 left of his original
investment. His shares dropped in value by 35% in 4 days. What amount did Alex pay for his shares
to being with?
Answer:
Let's start by using algebra to solve for the original amount that Alex paid for his shares.
Let X be the original amount that Alex paid for his shares.
We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:
0.65X = $72,800
Solving for X:
X = $72,800 / 0.65
X = $112,000
Therefore, Alex paid $112,000 for his shares to begin with.
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
Someone help i really need help with this
Answer:
35 pages per minute
Step-by-step explanation:
175/5= 35
Check
35 x 5 = 175
175/35= 5
The length of a particular animals pregnancies are approximately normally distributed, with a mean of 272 days and a standard deviation of 12 days.
A) what is the proportion of pregnancies that lasts more than 278 days?
B) what is the proportion of pregnancies lasts between 257 and 275 days?
C) what is the probability that a randomly selected pregnancy lasts no more than 266 days?
D) a “very preterm” baby is one whose gestation period is less than 242 days. Are very preterm babies unusual?
Answer:
To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.
A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.
B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.
C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.
D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.
Write two numbers that multiply to the value on top and add to the value on bottom.
8
8
−
6
−6
×
×
+
+
A population of values has a normal distribution with a mean of 246 and a standard deviation of 89.7. You intend to draw a random sample of size m = 158.
Answer the following, rounding your answers to three decimals where appropriate.
Find the probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4.
P(M>242.4) = ???
The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.
How to calculate the probabilityz = (x - μ) / (σ/√n)
where x is the sample mean.
Substituting the values, we get:
z = (242.4 - 246) / (89.7/√158) ≈ -0.670
We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.
P(z > -0.670) ≈ 0.751
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limit x->oo (sqrt(x^2-9x+1)-x)=?
I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.
Note that the limit of the expression as x approaches infinity is 1/2.
How did we arrive at this conclusion ?start by multiplying both the numerator and denominator by the conjugate expression
√ (x ² - 9x + 1) + x,
this will eliminates the root in the numerator
lim x->∞ [(√(x ² - 9x + 1) - x) * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)
Expanding the numerator
lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)
Simplifying further:
lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)
we can see that the 1/x ² term approaches zero, and the expression simplifies to
lim x->∞ [(1 - 0)] / (√(1 - 0) + 1)
= 1/2
So it is correct to state that the limit of the expression as x approaches infinity is 1/2.
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Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
Ox(x²-5) + 6(x² - 5)
Ox(x²+5)-6(x²+ 5)
O x²(x - 5) + 6(x - 5)
O x²(x+5)-6(x+ 5)
Answer:
x^2(x+5)-6(x+5)!!!!!!!!