Evaluate the expressions using the distributive property. ⅔(-7) + ⅔(-5)

The probability that the spinner lands on yellow and the coin toss is heads is 9/20.

To find the probability that the spinner lands on yellow and the coin toss is heads, we need to determine the probability of each event and then multiply them together.

The probability of the spinner landing on yellow is given by the number of yellow sections (18) divided by the total number of sections (20). Therefore, the probability of the spinner landing on yellow is 18/20 or 9/10.

The probability of the coin toss resulting in heads is 1/2 since there are two equally likely outcomes, heads and tails.

To find the probability of both events occurring together, we multiply the individual probabilities:

Probability (Spinner lands on yellow and Coin toss is heads) = Probability (Spinner lands on yellow) * Probability (Coin toss is heads)

= (9/10) * (1/2)

= 9/20

Therefore, nine out of twenty times, the spinner will fall on yellow and the coin will come up heads.

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The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

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Answer:

\( \boxed{x = 1.1614}\)

Step-by-step explanation:

\( \boxed{question \: \: 2.} \\ ( - 4 ) { \times 10}^{x} - 50 = - 108 \\ ( - 4 ) { \times 10}^{x} = - 58 \\ { 10}^{x} = \frac{ - 58}{ - 4} \\ {10}^{x} = 14.5 \\ x = log_{10}(14.5) \\ x = log(14.5) = 1.1613680022 \\ \boxed{x = 1.1613680022}\)

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Answer: monthly customer charge of $7.58 plus $0.08275 per kilowatt-hour (kWhr) for the first 400 kWhr

Step-by-step explanation: I took this test before so I hope this helps gl on the test

a) The charge for using 300 kWhr in a month is $ 32.41

b) The charge for using 700 kWhr in a month is $ 59.30

c) The rule for computing C is

    C ( x ) = { 7.58 + 0.08275x    if 0 ≤ x ≤ 400
                   15.848 + 0.06208x    if x > 400

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The monthly charge = $ 7.58

The monthly charge for per kWhr = $ 0.08275

The monthly charge per kWhr over 400 kWhr = $ 0.06208

So ,

The monthly charge for x kWhr is given by the equation = 7.58 + 0.08275x

The monthly charge for x kWhr which is more than 400 kWhr is given by the equation = 7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )

Now ,

a)

The charge for using 300 kWhr in a month is calculated by substituting the value of x as 300

So ,

The monthly charge for x kWhr is given by the equation = 7.58 + 0.08275x

The monthly charge for 300 kWhr = 7.58 + 0.08275 x 300

                                                         = 7.58 + 24.825

                                                         = $ 32.405

Therefore , The monthly charge for 300 kWhr is $ 32.41

b)

The charge for using 700 kWhr in a month is calculated by substituting the value for x as 700

The monthly charge for x kWhr which is more than 400 kWhr is given by the equation = 7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )

The monthly charge for 700 kWhr =  
7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )

Substituting the value for x as 700 , we get

= 7.58 + 0.08275 ( 400 ) + 0.06208 ( 300 )

= 40.68 + 18.624

= $ 59.304

Therefore , The monthly charge for 700 kWhr is $ 59.304

c)

Let x represent the number of kWhr used and C be the monthly charge for x kWhr.

The model can be split into 2 parts of condition , where

For , 0 ≤ x ≤ 400

The function is 7.58 + 0.08275x

For , x > 400

The function is 15.848 + 0.06208x

Therefore ,

The rule for computing C is

    C ( x ) = { 7.58 + 0.08275x    if 0 ≤ x ≤ 400
                   15.848 + 0.06208x    if x > 400

Hence , The monthly charge for 300 kWhr is $ 32.41 and the monthly charge for 700 kWhr is $ 59.304

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Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Answer:

$70.399.62

Step-by-step explanation:

To find the final amount, we have to use the compound interest formula

A = P(1 + r/n)ⁿˣ

A = Final amount

P = Starting amount (65,000)

r = rate (0.02)

n = time applied (4 since it's quarterly, meaning 4 times every year)

x = years (4)

Our equation will look like this

A = 65,000(1 + 0.02/4)¹⁶

You should use a calculator to plug to solve 65,000(1 + 0.02/4)¹⁶

A = 70,399.62483294155

Answer:

1.25

Step-by-step explanation:

1.5 divided by 1.2 is 1.25

Hope this helps☺️

Answer:

1.25

Step-by-step explanation:

1.5 / 1.2 = 15/12 = 5/4 = 1 1/4 = 1.25

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer:

5

Step-by-step explanation:

Turn 3 1/3 into an improper fraction.

Multiply the denominator by the whole number.

9

Add the numerator.

10/3

Now we flip 2/3 to be 3/2

Multiply 10/3 by 3/2

30/6

Simplify.

5

Hope I helped :)

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Answer:

5

Step-by-step explanation:

Answer:

y = -5/4x -4

Step-by-step explanation:

slope(m)= -5/4

x1=-4,y1=1

using the formula for one point form

y-y1=m(x-x1)

y-1= -5/4(x-(-4))

y-1 = -5/4x + -5/4 × +4

y - 1 = -5/4x -5

y=-5/4x -5 + 1

y = -5/4x -4.

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Answer:

4 minutes and 44 seconds.

Answer:

B, 6 x 30

Step-by-step explanation:

Because that's the only answer.

Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Answer:

The answer is 5 and 10.hbbbb

Answer:

graph the line -2x+3 as a dotted line and shade in below that line.

Step-by-step explanation:

Linear inequalities are an inequality... which contain linear equations. To graph these linear inequalities it helps to first just graph the linear equation and then based on the inequality whether it's less than, less than or equal to, greater than, or greater than or equal to we would draw above or below this line and with a solid or dotted line.

So we're given the equation: \(y < -2x+3\) it helps to first just graph the -2x + 3, which we can do by starting at the y-intercept of 3 and then going down 2 and going right 1 as defined by the slope -2. Likewise we can go up 2 and go left 1 from the y-intercept to define points to the left of the y-axis.

Now from here we look at the inequality: \(y < -2x+3\), it's telling us y values less than -2x + 3, so we want to be below the line we just graphed, so shade below the line. One thing to note is it's a less than and not a less than or equal to so the line it self is not included, meaning we draw a dotted line.

I included a desmos graph which further illustrates how this would look.

Answer:

150

Step-by-step explanation:

Answer:

6 apples per pie

Step-by-step explanation:

2x+7=19

x=# of apples per pie

Subtract 7 from both sides:

2x=12

Divide both sides by 2:

x=6

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

y = 67.19

Step-by-step explanation:

y/5.6 = 12

=> y = 12(5.6)

=> y = 67.19

Answer:

1/8

Step-by-step explanation:

Suppose there are 7 males so there will be 1 female according to the question.

So there is 1 female out of a total of 8 students. So the answer is 1/8.

Because the female is 1 out of the 8 people.

Answer:

\( Range =1.41-0.66 = 0.75\)

\( \bar X = 1.171 W/Kg\)

\( s^2 = 0.0607\)

And taking the square root we got the sample deviation:

\( s = \sqrt{0.0607}= 0.246 W/kg\)

Step-by-step explanation:

For this case we have the following datset given:

0.83 1.39 1.39 1.03 0.66 1.26 1.39 1.18 1.41 1.19 1.15

We need to find the range, and the range is defined by:

\( Range = Max -Min\)

And replacinng we got:

\( Range =1.41-0.66 = 0.75\)

Then we can find the sample variance, but firt we need to find the sample mean with this formula:

\(\bar X = \frac{\sum_{i=1}^n X_i}{n}\)

And replacing we got:

\( \bar X = 1.171 W/Kg\)

Now we can find the sample variance with this formula:

\( s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}\)

And replacing we got:

\( s^2 = 0.0607\)

And taking the square root we got the sample deviation:

\( s = \sqrt{0.0607}= 0.246 W/kg\)

Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²