Suppose y varies directly as x, and y = 7 when x = 2. Find x when y = 21.

Answer:

12:35

Step-by-step explanation:

Answer:

elaborate

Step-by-step explanation:

Answer: 127

Step-by-step explanation:

<TWV is the sum of the other 2 angles.  Create your equation

<UWV + <TWU = < TWV

n + 45 + 8n + 127 = -10n +77               >Combine like terms

9n + 172 = -10n +77                             > add 10n to both sides

19n +172 = 77                                        >Subtract 172 from both sides

19n = -95                                              >Divide by 19 to both sides

n= -5                                                     >plug back in to find angle

<TWV = -10n +77

<TWV =  -10(-5) +77

<TWV = 127

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Volume of a rectangular solid = Length x breadth x height

=(a+2) x (a+4) x (3a)

=(a+2)(a+4)(3a)

Answer:

Will you help me plz I will follow you

Answer:

5/24 of a bag I just had this question an thought I'd help you

Answer:

Option B is correct

Step-by-step explanation:

Given: \(\left | p \right |=7\sqrt{2}\,,\,\left | p+q \right |=12\sqrt{3}\)

To find: interval on which \(\left | q \right |\) must fall

Solution:

\(\left | p \right |=7\sqrt{2}\\-7\sqrt{2}\leq p\leq 7\sqrt{2}\,\,(i)\)

\(\left | p+q \right |=12\sqrt{3}\\-12\sqrt{3}\leq p+q\leq 12\sqrt{3}\,\,(ii)\)

Subtract (ii) from (i)

\(-12\sqrt{3}+7\sqrt{2}\leq p+q-p\leq 12\sqrt{3}-7\sqrt{2}\\-12\sqrt{3}+7\sqrt{2}\leq q\leq 12\sqrt{3}-7\sqrt{2}\\\left | q \right |=12\sqrt{3}-7\sqrt{2}\)

So, \(\left | q \right |\) must fall in interval \([12\sqrt{3}-7\sqrt{2},\infty)\)

Therefore, option B is correct.

According to the given statement The average value of the draw dollars is  $0.0662.

The average value of the draw can be calculated by finding the average value of each type of coin and then taking the weighted average based on the probability of picking each coin.
The value of a nickel is $0.05, the value of a dime is $0.10, and the value of a penny is $0.01.
To find the average value of the draw, we need to calculate the probability of picking each coin.
The total number of coins in the box is 6 + 8 + 12 = 26.
The probability of picking a nickel is 6/26, the probability of picking a dime is 8/26, and the probability of picking a penny is 12/26.
To calculate the average value of the draw, we multiply the value of each coin by its probability and then add them together.
(0.05 * 6/26) + (0.10 * 8/26) + (0.01 * 12/26)

= 0.0308 + 0.0308 + 0.0046

= 0.0662
Therefore, the average value of the draw is $0.0662.

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The average value of the draw can be calculated by finding the average value of each coin and then taking the weighted average based on the number of each coin in the box. When a coin is picked at random from the box, the average value of the draw is $0.047 per coin.

To find the average value of a nickel, dime, and penny, we need to know their respective values. A nickel is worth $0.05, a dime is worth $0.10, and a penny is worth $0.01.

Now, let's calculate the average value for each coin:
- For the 6 nickels, the total value is 6 * $0.05 = $0.30.
- For the 8 dimes, the total value is 8 * $0.10 = $0.80.
- For the 12 pennies, the total value is 12 * $0.01 = $0.12.

Next, we need to calculate the weighted average based on the number of each coin in the box.
- The total number of coins in the box is 6 + 8 + 12 = 26.

To calculate the weighted average, we divide the total value of all the coins by the total number of coins:
- Total value of all coins = $0.30 + $0.80 + $0.12 = $1.22.
- Average value of the draw = Total value of all coins / Total number of coins = $1.22 / 26 = $0.047 per coin.

Therefore, the average value of the draw in dollars is $0.047 per coin.

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Answer:

Step-by-step explanation:

389

Answer. 3/89

Step-by-step explanation:

HEY FREN

Answer:

you have to use the protractor tool

Answer:

It would take 15 years

Step-by-step explanation:

The length of time it takes to reach $1,000 savings can be determined from the future value formula given below:

FV=PV*(1+r/4)^n*4

FV is the target savings of $1,000

PV is the amount invested which is $600

r is the rate of interest of 3.4%

n is the unknown

1000=600*(1+3.4%/4)^4n

1000=600*(1+0.0085 )^4n

1000=600*(1.0085)^4n

1000/600=1.0085^4n

1.666666667 =1.0085^4n

take log of both sides

ln 1.666666667 =4n ln 1.0085

4n=ln 1.666666667/ln 1.0085

4n=0.510825624 /0.008464078

4n=60.35218768

n=60.35218768 /4

n= 15.09  

Answer:

6.25

Step-by-step explanation:

Answer:

5 inches is the length of each edge.

Step-by-step explanation:

³√125 = 5 inches.

Answer:

B

Step-by-step explanation:

21 inches to 7 inches

The width of the original image is B)  \(7\frac{7}{8}\) inches.

Given that: The width of the large poster is 21 inches.

Given that: The original image has dimensions that are 3/8 of the dimensions of the image in the poster.

So the width of the original image is = \(\frac{3}{8}\cdot21=\frac{63}{8}=7\frac{7}{8}\)

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Answer: -4.7 degrees Celsius

Step-by-step explanation:

-12.6 + 7.9 = -4.7

This is because 72/96 = 0.75 which converts to 75%

Answer:

75%

Step-by-step explanation:

Answer: D = 3c-5

Step-by-step explanation:

The first shape shows the input, C, the second one multiplies it by 3, next, it subtracts C by 5, leaving you with D equaling C times three, minus five.
You can simplify this equation into this:

D=3C (multiplied by 3)

Then subtract by 5
D=3C-5

Answer:

-8/3

Step-by-step explanation:

8x + 3y = -9    (subtract 8x from both sides)

3y = -8x-9       (divide by 3 on both sides)

y = (-8/3)x-3

    2. Identify the Slope

(-8/3) is the slope

Slope is the number before the x term

Hope this helps :)

Finding the area under a curve using technology requires knowledge of calculus or a graphing calculator with a built-in integral function.

We can use either method to find the area between the edge of the garden bed and the side of the house.

To find the area between the edge of the garden bed and the side of the house, we need to integrate the function that represents the distance between the two. In this case, the distance between the edge of the garden bed and the side of the house is given by the equation y = x + 1.

To integrate this function, we can use calculus or a graphing calculator with a built-in integral function. Calculus involves finding the antiderivative of the function, while a graphing calculator can use numerical methods to approximate the integral.

If using a graphing calculator, we can graph the function y = x + 1 and then use the integral function to find the area between the curve and the x-axis. The result will be the area between the edge of the garden bed and the side of the house, which can be used to calculate the amount of mulch needed for the job.

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The formula for the nth term of an arithmetic sequence is an = a1 + (n-1)d.

In an arithmetic sequence, the common difference is constant.

In finding the missing term or nth term of an arithmetic sequence, a refers to the term.

If the common difference between consecutive terms is negative, the sequence is decreasing.

In a geometric sequence, each term after the first can be obtained by multiplying the preceding term by a fixed constant.

Another term for a geometric sequence is a geometric progression.

To find the common ratio of the geometric sequence 9, -27, 81, -243, we divide each term by the preceding term:

-27/9 = -3

81/-27 = -3

-243/81 = -3

The common ratio is -3.

To find the three consecutive terms of a sequence with a1 = -11 and r = 3:

a1 = -11

a2 = a1 * r

= -11 * 3

= -33

a3 = a2 * r

= -33 * 3

= -99

The three consecutive terms are -11, -33, -99.

The given arithmetic sequence is 12, 18, 24, 30, ...

The common difference is d = 18 - 12 = 6.

The formula for the nth term of an arithmetic sequence is an = a1 + (n-1)d.

Plugging in the values, we get:

a12 = 12 + (12-1)6

= 12 + 11*6

= 12 + 66

= 78.

The 12th term of the arithmetic sequence is 78.

The first term of the sequence is -23 and the common difference is 5.

The formula for the nth term of an arithmetic sequence is an = a1 + (n-1)d.

Plugging in the values, we get:

a13 = -23 + (13-1)5

= -23 + 12*5

= -23 + 60

= 37.

The 13th term of the sequence is 37.

Let's assume the first term of the sequence is a1 and the common difference is d.

The seventh term of the sequence is given as 17, so we have:

a7 = a1 + 6d

= 17.

The eighth term of the sequence is given as 24, so we have:

a8 = a1 + 7d

= 24.

Now we can set up a system of equations and solve for a1 and d:

a1 + 6d = 17

a1 + 7d = 24

Subtracting the first equation from the second equation, we get:

d = 24 - 17 = 7

Substituting d = 7 into the first equation, we get:

a1 + 6(7) = 17

a1 + 42 = 17

a1 = 17 - 42

a1 = -25

Therefore, the value of a1 is -25 and the value of d is 7.

The common ratio of the geometric sequence 9, -27, 81, -243 is -3.

The three consecutive terms of a sequence with a1 = -11 and r = 3 are -11, -33, -99.

The formula for the nth term of the arithmetic sequence 12, 18, 24, 30, … is an = 12 + (n-1)6.

The 12th term of the arithmetic sequence 11, 16, 21, 26, … is 78.

The 13th term of the arithmetic sequence with the first term -23 and common difference 5 is 37.

The first term of the sequence with a seventh term of 17 and an eighth term of 24 is -25, and the common difference is 7.

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Answer:

The slope is -4

Step-by-step explanation:

hope this helps

(-7,21),(-6,17)

17-21/(-6)-(-7)

=-4/1

= -4

(-5,13),(-4,9)

9-13/(-4)-(-5)

=-4/1

= -4

The equation should be 105(0.15)+ x = 170 and the value of x is 154.25

Here we assume the hiking boots cost be x

So, the equation is

105(0.15) + x = 170

15.75 + x = 170

x = 170 - 15.75

x = 154.25

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

\( \frac{6}{x} = \frac{8}{24} \)

\(8x = 144\)

\(x = 18\)

\( \frac{8}{24} = \frac{y}{12} \)

\(24y = 96\)

\(y = 4\)

So x = 18 and y = 4.

A. Calculation of A for which f(x,y) is a valid joint probability density function The integral of the joint probability density function of the region must be equal to 1 for f(x,y) to be a joint probability density function.

∫∞0 ∫4.2.7 x f(x, y) dy dx = 1 ... Equation (1)

Since y varies from -0.7 to oo and x varies from 0.7 to oo, the integral can be computed as follows:∫∞0 ∫-0.7oo x (12x+5y-3) A dy dx = 1 ... Equation (2)

Evaluating the integral,∫∞0 x [∫-0.7oo (12x+5y-3) A dy] dx = 1A [x (6x - 1) [5y + 12x - 3] / 5 |_|-0.7oo dx = 1

Simplifying further,A [∫∞0 (x^2 (6x - 1)) / 5 dx + ∫∞0 (x (5y + 12x - 3) (-0.7)) / 5 dx] = 1

Evaluating the integral, we get, A [(2/35) + (-0.7 (27/10))] = 1

Hence, A = -1.0924B. Joint probability that x > 2 and y < 4 ∫∞2 ∫-0.7^45 (12x+5y-3) A dy dx

Since y varies from -0.7 to 4, and x varies from 2 to oo, the integral can be computed as follows:

∫∞2 ∫-0.7^4 (12x+5y-3) A dy dx = ∫∞2 A [y (12x + 5y - 3) / 2 |_|-0.7^4 dx]= ∫∞2 A [(2x (76.15)) / 2 - (4.35 (12x + 4.3)) / 2] dx= 57.74 ATherefore, the joint probability that x > 2 and y < 4 is 57.74 A.C.

Joint probability that x < 8 and y > 1∫8-0.7 ∫∞1 (12x+5y-3) A dy dx

Since y varies from 1 to oo and x varies from 0.7 to 8, the integral can be computed as follows:∫8-0.7 ∫∞1 (12x+5y-3) A dy dx = ∫8-0.7 A [y (12x + 5y - 3) / 2 |_|1^∞ dx] = ∫8-0.7 A [(58x - 62.65) / 2] dx= 1585.55 A

Therefore, the joint probability that x < 8 and y > 1 is 1585.55 A.D. Joint probability that x < 0.8 and y > -oo∫0.7-0.8 ∫-oo^∞ (12x+5y-3) A dy dxSince y varies from -oo to oo, and x varies from 0.7 to 0.8, the integral can be computed as follows:∫0.7-0.8 ∫-oo^∞ (12x+5y-3) A dy dx = ∫0.7-0.8 A [(5y (x - 4) - 3y) / 5 |_|-oo^∞ dx] = 0

Therefore, the joint probability that x < 0.8 and y > -oo is 0.E. Expected value of XY i.e. E[XY]

The expected value of XY is given by

∫∞0 ∫-0.7^4 xy (12x+5y-3) A dy dx= ∫∞0 [(12x (x^2 / 2) / 3 + 5x (∫-0.7^4 y^2 / 2 dy) / 3 - 3x (y / 2) |_|-0.7^4) A dx] ... Equation (3)Evaluating the integral, we get,E[XY] = 49.87 A

Therefore, the expected value of XY i.e. E[XY] is 49.87 A.

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The joint probability that x < 0.8 and y > - ∞ is 6/5 and the expected value of XY is given by E[XY] = 135/22

The random variables X and Y have a joint probability density function of the form

\(-(12x+5y-3) f(x, y) = Ae\)

Where x is valid from 0.7 to oo and y is valid from -0.7 to o

(A) As per the probability density function, the integral of f(x, y) should be equal to 1.

\(∫∞-∞∫∞-0.712x+5y-3 dxdy = 1∫∞-∞(12x+5y-3)/2 dx dy = 1(∫∞-∞12x/2dx) (∫∞-∞5y/2 dy) (∫∞-∞(-3)/2 dx dy)= 1(6∞) (25/2) (3) = ∞\), which is not possible.

Therefore, no value of A can make f(x, y) a valid joint probability density function.

(B) The probability that x > 2 and y < 4 is given by

\(∫4-0.7∫∞21-(12x+5y-3) dxdy = A∫4-0.7(6-12x-5y)dx dy = A[(-105/4)] = 1A = -4/105\)

Thus the joint probability that x > 2 and y < 4 is

\(∫4-0.7∫∞212x+5y-3 dxdy = -4/105 ∫4-0.7(6-12x-5y)dxdy= 0.5\)

(C) The probability that x < 8 and y > 1 is given by

\(∫∞1∫80.712x+5y-3 dxdy = A∫∞112x-3 dx ∫88-5y/2dy = A[(-197/40)(49/10)] = 1A = -400/1970\)

Thus the joint probability that x < 8 and y > 1 is

\(∫∞1∫88-0.712x+5y-3 dxdy = -400/1970∫∞1(12x-3)(5y-8) dydx= 343/197\)

(D) The probability that x < 0.8 and y > - ∞ is given by

\(∫∞-∞∫0.8-0.712x+5y-3 dxdy = A∫∞-∞(-12x+5y+3)/2 dx dy = A[(3/2)(5/2)]= 15/4AA = 4/15\)

Thus the joint probability that x < 0.8 and y > - ∞ is

\(∫∞-∞∫0.8-0.712x+5y-3 dxdy = 4/15 ∫∞-∞(-12x+5y+3)dxdy = 6/5\)

(E) The expected value of XY is given by

\(E[XY] = ∫∞-∞∫∞-0.7xy(12x+5y-3) dx dy= 135/22\)

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2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.

First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.

To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.

To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.

Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.

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Answer:

25,45,5

Step-by-step explanation:

The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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