-8x - 2y = -24
Find the slope

The Answer is: 20% . Chapter 1 Daily Value Practice Problems

The percentage of your daily value would equal 20%.

Given that, you need 2300 calories a day but you want to go on a lower carbohydrate eating plan. So you decide to get 40% of your calories from carbs.

Daily values are the recommended amounts of nutrients to consume or not to exceed each day and the DV% is how much a nutrient in a single serving of an individually packaged food or dietary supplement contributes to your daily diet. For example, if the DV for a certain nutrient is 300 micrograms and a packaged food or supplement has 30 mcg in one serving, the % DV for that nutrient in a serving of the product would be 10%.

According to the question, a person needs 2300 calories a day but because of this limited diet plan, he takes only 40% calories from carbohydrates.

Therefore, the calories needed for his diet=2300*40%

=2300*0.4

=920

The calories get by him after one serving of frosted mini wheat=48 gm of carbohydrates

1 gm of carbohydrates=4 calories

calories intake by him from carbohydrates=48*4

=192

% of his daily value=192/920*100

=0.208*100

=20.8=20%

Therefore, the percentage of your daily value would equal 20%.

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Answer:

There are a total of 14 tickets in the raffle, and two of them will be selected as the winners of the first and second prizes.

The probability that you win the first prize is 1/14, since there is only one winning ticket out of 14 tickets. After your ticket is drawn as the winner of the first prize, there are only 13 tickets left, one of which is your friend's ticket.

The probability that your friend wins the second prize, given that you have already won the first prize, is 1/13, since there is only one winning ticket left out of the 13 remaining tickets.

Therefore, the exact probability that you win the first prize and your friend wins the second prize is:

(1/14) * (1/13) = 1/182

So the probability is 1 out of 182, or approximately 0.0055, or 0.55%

Step-by-step explanation:

Answer:

\(\sf Probability=\dfrac{1}{182}\)

Step-by-step explanation:

Given you and a friend each buy a raffle ticket along with 12 other people:

\(\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}\)

The first prize is the first raffle ticket drawn. Therefore, the probability of winning the first prize is:

    \(\sf \bullet \quad P(first\;prize)=\dfrac{1}{14}\)

After the first raffle ticket is drawn, there are a total of 13 raffle tickets remaining.

The second prize is the next raffle ticket drawn. Therefore, the probability of winning the second prize is:

    \(\sf \bullet \quad P(first\;prize)=\dfrac{1}{13}\)

To calculate the exact probability that you win the first prize and your friend wins the second prize, multiply the found probabilities:

\(\implies \sf Probability=\dfrac{1}{14}\times\dfrac{1}{13}\)

\(\implies \sf Probability=\dfrac{1}{182}\)

Therefore, the exact probability that you win the first prize and your friend wins the second prize is:

    \(\bullet \quad \sf \dfrac{1}{182}\)

Answer:

21a + 77b

Step-by-step explanation:

multiply 7 by the first variable in parenthesis

7 × 3a = 21a

multiply 7 by the second variable in parenthesis

7 × 11b = 77b

combine

21a + 77b

have a lovely day <3

\(\frac{x}{3x}+\frac{8x}{3x}=\frac{1}{3}+\frac{8}{3}=3\)

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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3 snacks

Let the number of snacks Deborah bought be "x"

Given the following parameters:

Cost of her ticket = $11.50

Cost of "x" snacks = $2.50x

If the amount she spent in total is $19, the required equation that represents the situation will be expressed as:

2.50x + 11.50 = 19

Subtract 11.50 from both sides

2.50x + 11.50 - 11.50 = 19 - 11.50

2.50x = 19 - 11.50

2.50x = 7.50

Divide both sides by 2.50

2.50x/2.50 = 7.50/2.50

x = 7.50/2.50

x = 3

Therefore the amount of snacks she bought is 3 snacks

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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No, there are x values which map to more than 1 y-value.

Given that Matthew examines the relation as shown in the below.

{(4, -11), (3,1), (0,1), (2,6), (3, -1)}

We need to check whether the relation is a function or not,

So, we know that,

A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.

If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.

Here we can see that the y values are repeated, so it is not a function.

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The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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The original amount of the sale is $165

The given parameters are:

Bill after discount = $140

Discount = 15%

The original amount of the sale is calculated as:

Bill after discount = original amount * (1 - Discount)

So, we have:

140 = original amount * (1 - 15%)

This gives:

140 = original amount * 0.85

Divide by 0.85

Original amount = 165

Hence, the original amount of the sale is $165

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If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.

Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.

This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.

Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.

Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.

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Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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Step-by-step explanation:

10 × n = 360

n = 360 ÷ 10

n = 36

So, n = 36

(3 × 4) × 5 = k × (5 × 4)

12 × 5 = k × 20

60 = k × 20

k = 60 ÷ 20

k = 3

So, k = 3

Answer:

\(n = 36 \\ k = 3\)

Step-by-step explanation:

#1

\(10 \times n = 360 \\ 10n = 360 \\ \frac{10n}{10} = \frac{360}{10} \\ n = 36\)

#2

\((3 \times 4) \times 5 = k \times (5 \times 4) \\ 12 \times 5 = k \times 20 \\ 60 = 20k \\ \frac{60}{20} = \frac{20k}{20} \\ 3 = k\)

Hope this helps you.

Let me know if you have any other questions:-)

We can use the points given to solve for the slope.

Slope formula: y2-y1/x2-x1

7-3/4-1

4/3

Find the y-intercept.

y = mx + b

3 = 4/3(1) + b

3 = 4/3 + b

5/3 = b

The slope of a perpendicular line is the opposite and reciprocal.

4/3 -> -3/4

Write the new equation.

y = -3/4x + 5/3

Best of Luck!

The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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Answer:

900 people surveyed.

Step-by-step explanation:

To solve this problem, let's set up a proportion.

60% = 6/10

Let x represent the total amount of people surveyed (or what we are trying to find)

6/10 = 540/x

To solve this proportion, let's use cross products, or the multiplication of the numerator of one fraction times the denominator of the other fraction and setting them equal to one another.

10(540) = x(6)

Now, let's simplify the resulting equation.

5400 = 6x

Now, let's divide both sides by 6, or the coefficient of x, to get it alone on the right side of the equation.

x= 900

Therefore, if 540 people preferred walking, then 900 people were surveyed.

Answer:

please tell me if there iscany sing after 4xy

Answer:

xy-x+y+1

Step-by-step explanation:

(1-x^2)(1-y^2)+4xy=1-y^2-x^2+x^2y^2+4xy

here, 4xy=2xy+2xy

then, -(x^2-2xy+y^2)+(x^2y^2+2xy+1)=-(x-y)^2+(xy+1)^2

by a^2-b^2=(a+b)(a-b)

(xy+1+x-y)(xy+1-x+y)

1-2x+y-x^2y+x^2=-y(x^2-1)+(x^2-2x+1)=-y(x+1)(x-1)+(x-1)^2

=(x-1)(x-1-xy-y)=-(x-1)(xy-x+y+1)

thus, common factor is xy-x+y+1

Hope this helps

Answer:

Step-by-step explanation:

f(x) = x^2

reflect along the x-axis

g(x) = -x^2

expand vertilcally by a factor of 1/3

g(x) = (-1/3) x^2

move horizontally 4 units to the left

g(x) = (-1/3) (x+4)^2

hope this helps

Answer:

B. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 4 units to the left.

Step-by-step explanation:

The \(\frac{-1}{3}\) is less than one, making it stretch wider, and the (-) made it flip over the x-axis. The +4 in \((x+4)^2\) made the function on the graph shift 4 units to the left.

This makes the correct answer be "B."

Answer:

6 candies

Step-by-step explanation:

(find unit rate, cost / quantity)

35/10 = 3.5

20/3.5 = = 5.7142857142857

candies cannot be in decimal so you must round to the nearest whole

Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.

It should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:

= ✓(0.35² + 0.65²)

= 0.76 miles.

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Answer:

07

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

V = 5

I = 1

V + I + I = 5 + 1 + 1 = 7

Hope that helps

According to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

Since p:q:r = √3:1:1, we can write:

p = √3x

q = x

r = x

where x is a common factor.

We can see that triangle ABC is a 30-60-90 triangle with angle A = 60 degrees, and that angle BOC is a right angle. Therefore, we can use the ratios of sides in a 30-60-90 triangle to find the values of P, O, and R:

P = AB = p = √3x

O = BC/2 = q/2 = x/2

R = AC = r = x

Therefore, the ratio P:O:R is:

P:O:R = √3x : x/2 : x

We can simplify this ratio by multiplying all terms by 2 to get rid of the fraction:

2√3x : x : 2x

We can further simplify by dividing all terms by x:

2√3 : 1 : 2

Therefore, according to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

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Answer:

C and E

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

The total number of marbles is 2 + 2 + 3+ 5 = 12

the number of green ones is 3

So the probability of green = 3/12 = 1/4 = 0.25

Answer:

Red

Step-by-step explanation:

Because it was most pick the first time

The mathematical model that represents the general price movement of mortgages is:     ΔPM = f(Δk, ΔPrin, ΔC)

Where ΔPM is the change in the price of the mortgage, Δk is the change in the required rate of return, ΔPrin is the change in the principal payment, and ΔC is the change in the interest payment.

This means that the change in the price of a mortgage is a function of the change in the required rate of return, the change in the principal payment, and the change in the interest payment.

The securities that are issued to financial institutions to increase liquidity in the secondary mortgage market by financing the origination of mortgages are:

Financial institutions may also receive private-label pass-through securities, although these are not guaranteed by government entities like Ginnie Mae, Freddie Mac, or Fannie Mae.

They are not backed by the government, but by private institutions, which can make them riskier.

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The ingredients I had left over were 1 cup of almonds, 1/2 cup of oats, 1/4 cup of coconut, 1/4 cup of honey, and 1/4 cup of chocolate chips.

Generally, I do feel like my plan was effective in maximizing my ingredients because I used all of the ingredients in the recipe and I also thought about how to use the ingredients in the most efficient way.

A different way I could have approached this problem would have been to make a granola bar that used the same ingredients but different proportions.

For example, instead of using 1/4 cup of honey I could have used 1/8 cup of honey and added 1/8 cup of peanut butter to the mix. This would have resulted in a different flavor and texture of the granola bar.

Additionally, I could have added other ingredients such as dried fruits or nuts to the mix to further enhance the flavor and texture of the granola bar.

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Answer:

----------------------

If the system of linear equations has infinitely many solutions, it means the two lines overlap.

In other words, each point of one of the lines also belongs to the second line.

Choices a, b, c  give us one or no solutions and therefore not the answer.

Choice d is reflecting the infinitely many solutions and hence is the correct one.

Answer:5

Step-by-step explanation:

5098