Gary, Mary, and Rory have 96 candies altogether.
Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".
After Gary gives Mary half of all his candies, he would have x/2 candies.
Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.
And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.
Now, we know that Gary would have 12 more candies than he had originally, which means:
x/2 + x/8 = x/2 + x/4 - 12
We can combine like terms and simplify the equation:
x/2 + x/8 = x/4 + x/4 - 12
x/8 = 12
x = 8 * 12
x = 96
Thus, Gary, Mary, and Rory have 96 candies altogether.
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Solve the proportion.
8 / 3 = g / 3
a. 1 / 8
b. 9 / 8
c. 8
d. 8 / 9
How do you make a truth table?
If we want to create a truth table , for say expression (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.
Truth table is a medium used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.
On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.
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Pls solve this 15 points
Answer:
128
Step-by-step explanation:
1/3base area×height
Write the simplified expression: 2x + 3(x - 2) - 3(x -6)
Answer:
2x+12
Step-by-step explanation:
2x+3(x−2)−3(x−6)
Distribute:
=2x+(3)(x)+(3)(−2)+(−3)(x)+(−3)(−6)
=2x+3x+−6+−3x+18
Combine Like Terms:
=2x+3x+−6+−3x+18
=(2x+3x+−3x)+(−6+18)
=2x+12
Answer:
=2x+12
Answer:
2x + 12
Step-by-step explanation:
distribute numbers inside parentheses
2x + 3x -6 -3x + 18
add x values together and integers together
2x + 3x -3x = 2x
-6 + 18 = 10
simplified to 2x + 12
If θ is an angle in standard position and its terminal side passes through the point (-3,4), find the exact value of tanθ in simplest radical form.
Answer:
so x = 20 , y = -21 , which is in quad IV
r^2= 400+441 = 841
r = √841 = 29
then cos Ø = 20/29
sec Ø = 29/20 = 1.45
Step-by-step explanation:
please give brainliest
What is the perimeter of kite KLMN? StartRoot 2 EndRoot + StartRoot 5 EndRoot units StartRoot 14 EndRoot units 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units 4 StartRoot 5 EndRoot units
HELP PLEEEEAASEEE
Answer:
C. 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
Step-by-step explanation:
Answer:
The Answer is C.
Step-by-step explanation:
2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
pls help with this its due today
Using PEMDAS to solve the algebraic expression, the value is 2
What is Mathematical OperationMathematical operations are operations that involve the manipulation of numbers, variables, and/or equations. Examples of mathematical operations include addition, subtraction, multiplication, division, exponentiation, and root extraction.
In this problem, we can use PEMDAS to solve this algebraic expression.
[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3 (1/3)] + [6(3/4) + 5(1/2)] / 26 ÷ 3(5/7)] - 0.05
This will become;
[10.2 / 34] + [12.25 / 7] - 0.05
Dividing and adding the numbers will give us;
(0.3 + 1.75) - 0.05 = 2
The value is 2
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A storage space in a basement is in the shape of a rectangular prism. The height of the storage space is 5 feet. The length is seven times the width. The volume of the storage space is 595 cubic feet. Find the width and length of the storage space.
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same question buts its answered on the link above
7. A stock is worth $21. Its value is increasing at a rate of $0. 25 per week a.
Write an equation for the value y (in dollars) of the stock after x weeks.
b. If this trend would continue, what would be the value of the stock after 20 weeks?
The Equation for the value y is a. y = 21 + 0.25x (where x represents the number of weeks)
b. The value of the stock after 20 weeks would be 21 + (0.25 * 20) = $26.
This equation represents the linear relationship between the value of the stock (y) and the number of weeks (x). The value of the stock is initially $21, and it increases by $0.25 every week. This is represented by the coefficient of x (0.25) in the equation. By plugging in x=20 into the equation, we can find that after 20 weeks, the value of the stock would be $26. This is assuming that the rate of increase remains constant over time.
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1.) Select all shapes that are quadrilaterals. A D C С B H E G F
To indirectly measure the distance across a river, Houa stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Houa draws the diagram below to show the lengths and angles that she measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
According to the Houa's drawing the distance across the river PR is
198.95 feetHow to measure the distance PRThe length of line PR is calculated using the knowledge of similar triangles
While similar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent.
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shown, the pair of equivalent sides are
PO and OC, PR and RE,
The solution is worked out using sides PO and OC, PR and RE,
PO / OC = PR / RE
let PR be equal to y such that PO = 140 + y
(140 + y) / 230 = y / 135
cross multiplying
135(140 + y) = 230y
Expanding
18900 + 135y = 230y
collecting like terms
18900 = 230y - 135y
95y = 18900
y = 198.95 feet
Hence PR = 198.95 feet
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How do you find the mean and standard deviation of a simple random sample?
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
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If you have 10 friends and make two equal teams, what fraction do you use?
Plz help
In 1 week, Kim jogged 5.6 miles. She increased the distance she jogged each week by 3/4 mile. At the end of 5 weeks, how many total miles had Kim jogged?
A. 21.0 miles
B. 29.9 miles
C. 35.5 miles
D. 39.3 miles
Answer: the answer is 19.6
Step-by-step explanation:
just add up by each number, for example 5.6+3 miles is 8.6 miles so just keep adding up the miles to get this answer
Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
(p-value of 1 - (0.05/2)).
Hence the decision rule is given as follows:
|z| < 1.96 -> do not reject the null hypothesis -> not enough evidence.|z| > 1.96 -> reject the null hypothesis -> enough evidence.What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is of:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]
z = 1.24.
|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
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i need help fr fr like my mind honestly went blank
Answer:
894 mi²
Step-by-step explanation:
the area of parallelogram= base x height= 24mi x 37.25mi = 894 mi²
Tyrese works each day and earns more money per hour the longer he works. Write a function to represent a starting pay of $20 with an increase each hour by 3%. Determine the range of the amount Tyrese makes each hour if he can only work a total of 8 hours.
The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80
What is a range?The range is the space between the highest and lowest numbers.
Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.
To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.
The beginning wage is $20.
Suppose x hours are in a day.
A $20 salary is offered, with a 3% hourly raise.
e.g., increment = (3/100)*20*x = (3/5)x
A function's maximum possible earnings are
y = 20 + (3/5)x
He is only allowed to work a total of 8 hours, per our instructions.
Therefore, the most money she can make in 8 hours is
y = 20 + (3/5)*8
y = 20 + 4.8
y = 24*8
$20 is the first sum.
As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .
Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.
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I need help for number 2
The measure of the exterior angle for Object 1 - a decagon is 36°, while th measure of the exterior angle for Object 2 - a dodecagon is 30°.
What is a Decagon and a Dodecagon?n object with 12 sides is called a dodecagon while an object with 10 sides is called a decagon.
Note that the exterior angles of all shapes, regular or irregular is 360°. In this case, the shapes are regular, which means that the sides are equal, hence their angles will be equal.
To derive the exterior angle of a regular geometric shape, the formula is given as:
Exterior angle measure = 360 / number of sides
Hence for A (the decagon), we have:
EAM = 360/10
= 36°
For B (the dodecagon) we have:
EAM = 360/12
= 30°
Thus the exterior angle for both shapes are 36° and 30° respectively.
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what is the slope and y-intercept for y=1/2+4x
Answer:
- 1/4 slope
y-intercept: 2
pls mark me brainless if im right.
Given P(A) = 0.32, P(B) = 0.2 and P(AU B) = 0.366, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
By using formula, P(A n B) = 0.346. Rounded to the nearest thousandth, P(A n B) = 0.346
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between 0 and 1, the closer the probability is to 1, the more likely the event is to occur. The probability of an event is usually represented by the letter P, followed by the event in parentheses.
What is rounding off?Rounding off is a mathematical operation that is used to reduce the number of digits in a number while maintaining its value within a certain degree of accuracy. When we round off a number, we look at the digit that is immediately to the right of the last digit that we want to keep. If the number is less than 5, we keep the last digit as it is, but if the number is greater than or equal to 5, we add 1 to the last digit.
We can use the formula of conditional probability to find the value of P(A n B).
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
So we can substitute this in the first equation:
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
P(An B) = P(A U B) - P(A) - P(B) + P(An B)
Now we can substitute the given values:
P(An B) = 0.366 - 0.32 - 0.2 + P(An B)
P(An B) = 0.346 + P(An B)
To find P(An B) we can subtract 0.346 from both sides of the equation:
P(An B) = P(An B) - 0.346
P(An B) = P(An B) - 0.346
So, P(An B) = 0.346
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Abby works in the sales department. This month the company is offering a 3-week paid vacation to every employee who sells 230% of the amount sold last month. If Abby sold $480 products last month, how much does she need to sell this month to earn the vacation
well, what's 230% of $480?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{230\% of 480}}{\left( \cfrac{230}{100} \right)480}\implies \text{\LARGE 1104}[/tex]
Simplify the polynomial.
3x2 – 2x + 4x2 – X+X
Answer:
[tex]7x^{2} - 2x[/tex]
Step-by-step explanation:
combine like terms. not trying to be mean, but that all you have to do.
Answer:
14-2x
Step-by-step explanation:
collect like terms
3×2+4×2-2x-x-x
6+8-2x
=14-2x
Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie
Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nathan had 58 pieces of gum that he wants to make last six days.
Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,
= (58/6).
= 9.66 chewing gums but it should be a whole number.
So, Nathan can chew between 9 to 10 chewing gums each day.
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PLEASE HELP SOON
1. Solve the system. 3x+y = 10 y = 6x+1 Enter your answer by filling in the blanks. The solution is ( , )
2. Solve the system. 6x - y = -15 x + 2y = 17 Enter your answer as a coordinate pair in the blank.
Answer:
1. ( 1,7)
2. (17, 39)
Step-by-step explanation:
1. Replace all occurrences of y with 6x+1, and we get
9x + 1 = 10
x = 1
y = 6x + 1
y = 7
So, the answer for number 1 is (1,7)
2. 6x - y = -15x + 2y = 17
We subtract 2y and get
6x - 3y = 15x = 17
Replace all occurrences of x with 17, and we get
102 −3y = −15
x = 17
y = 39
So, the answer for number 2 is (17, 39)
Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend. please
help it's due tomorrow
Answer:
that is the persons username I got it from
Step-by-step explanation:
3 and 7
6 and 14
9 and 21
12 and 28
15 and 35
Step-by-step explanation:
If the two numbers they give you are 9 and 21, then the cranberry's are 3 ounces and the apples are 7 fliud ounces, then you can divide and multiply them to your will.
whats the answer for this question i need help
The answer for it is r = -4 :))
PLEASE HELP!!! I WILL MARK BRAINLEST. please help me guys
A store that specializes in shipping packages reports that the distribution of packages shipped during the winter holidays is normally distributed with a mean of 4. 5 pounds with a standard deviation of 1. 8 pounds
What is the probability that two randomly selected packages are both more than 4. 5 pounds? (assume the packages are independent of each other)
a. ) 0. 5
b. ) 1
c. ) 0
d. ) 0. 25
The correct option is option (d).
To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.
The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.
The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.
Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.
Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.
In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25
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In an inverse variation, y = 3 when x = 8. Write an inverse variation equation that shows
the relationship between x and y.
Write the equation using a decimal or an integer.
How do I find this?
Answer:
y = 24/xStep-by-step explanation:
An inverse variation equation is:
y = k/xWe have y = 3 when x = 8, find the coefficient k:
3 = k/8k = 3*8k = 24The equation is:
y = 24/xMai bought some party supplies from an online store. For shipping, the shop charges a flat fee of $7.95 or 6.25% of the total purchase, whichever is greater. Suppose Mai's total purchase is $128. How much shipping will she pay?
Answer:
8
Step-by-step explanation:
if we do 128+7.95 we get 135.95. but when we do 128+8(wich is 6.25% of 128) we get 136. so she will pay 8 dollars in shipping
Hope this helps.