In a standard deck of cards, the jack, queen, and king are "face cards." you draw a card from a standard deck. your friend peeks and lets you know that your card is a face card. what is the probability that it is not a king given that it is a face card? leave your answer as a fraction

The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.

Given that, Jimmy backpack is 60 cubic liters. He has a pile of equipment that takes up 43 cubic liters and then he has his sleeping bag that takes up 23 cubic liters.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let r be the amount of room left in his backpack.

Total space in backpack = A pile of equipment +  Sleeping bag + Room left

So, 60 = 43+23+r

The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.

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If Sam has 6 different hats and 3 different scarves, the number of combinations he could wear is: 18 ways.

Given the following data:

In this exercise, the number of ways 6 different hats and 3 different scarves can be worn without any form of repetition should be calculated by using a combination.

Mathematically, combination is given by this formula:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Where:

For Sam's combination:

[tex]_hC_s = 6 \times 3[/tex]

Sam = 18 ways.

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Answer:

[tex]x=\frac{225}{16}[/tex] is an extraneous solution.      

Step-by-step explanation:

Given : Equation [tex]-4\sqrt x-3=12[/tex]

To find : Solve for x and identify if it is an extraneous solution?

Solution :

Step 1 - Write the equation,

[tex]-4\sqrt x-3=12[/tex]

Step 2 - Add 3 both sides,

[tex]-4\sqrt x-3+3=12+3[/tex]

[tex]-4\sqrt x=15[/tex]

Step 3 - Squaring both sides,

[tex](-4\sqrt x)^2=(15)^2[/tex]

[tex]16x=225[/tex]

Step 4 - Divide both side by 16,

[tex]\frac{16}{16}x=\frac{225}{16}[/tex]

[tex]x=\frac{225}{16}[/tex]

For extraneous solution, Substitute the value of x back in the equation.

[tex] -4\sqrt (\frac{225}{16})-3=12[/tex]

[tex]-4\times\frac{15}{4}-3=12[/tex]

 [tex]-15-3=12[/tex]

[tex]-18\neq12[/tex]

The value of x does not satisfy the equation which means the value of x is an extraneous solution.

So, [tex]x=\frac{225}{16}[/tex] is an extraneous solution.

Jed and Alex do not shoot free throws at the same rate, Jed is faster by 0.5 seconds.

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, Jed took 2 free throws in 5 seconds.

∴ Jed can do 1 free throw in (5/2) = 2.5 seconds.

Alex took 4 free throws in 12 seconds.

∴ Alex can do 1 free throw in (12/4) = 3 seconds.

No, Jade and Alex do not shoot free throws at the same rate Jed is faster by 0.5 seconds.

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Final answer:

Janelle should plan to spend 3 hours walking back.

Explanation:

To find out how long Janelle should plan to spend walking back, we need to calculate the total time it takes her to run and walk. Since she runs at a speed of 7mph, she completes the distance of the race in 1 hour (4 miles / 7mph = 0.57 hours = 1 hour). Therefore, she spends 1 hour running and 3 hours left for walking. To find out the distance she walks back, we use the formula distance = speed x time. Since she walks at a speed of 3mph, the distance she walks back is 3mph x 3 hours = 9 miles.

Answer:

A

Step-by-step explanation:

Answer:

Options 1,2 and 4 are correct.

Step-by-step explanation:

We have been given a parallelogram MNPQ was dilated to create parallelogram  M'N'P'Q' and we asked to find out which of the given options are correct.

Let us see all the options one by one.

On using distance formula we can see that side MN is 2 units.

[tex]MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]

[tex]MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }[/tex]

[tex]MN=\sqrt{(2)^{2} } =2[/tex]

Therefore,option 1 is correct.

We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.

Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.

Now look at our option 4.

Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.

Therefore, option 4 is correct indeed.

Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.

Therefore, our fifth option is false.

Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

Slope = vertical distance / horizontal distance = change in y / change in x.

Scale factor = length of image/corresponding length of pre-image.

Find the length of MN:

MN = |4 - 2| = 2 units (Option A is true).

Find M'N':

M'N' = |10 - 5| = 5 units (Option B is true).

MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).

Find Slope of MQ:

Slope = 1/1 = 1

Find Slope of M'Q':

Slope = 2/2 = 1 (Option D is true).

Find the scale factor:

Scale factor = dimension of image/dimension of pre-image = M'N'/MN

Scale factor = 5/2 (Option E is NOT true).

Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

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Answer:

Step-by-step explanation:

[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]

[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]

[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]

[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]

Answer:

6

Step-by-step explanation:

The requried fraction of the bouquet that is pink roses is 7/12, as of the given proportion.

If Angelica's bouquet of a dozen roses contains 5 white roses, then the remaining roses must be pink. Since there are 12 roses in a dozen, the number of pink roses in the bouquet would be 12 - 5 = 7.

To find the fraction of the bouquet that is pink roses, we divide the number of pink roses by the total number of roses:

Fraction of pink roses = Number of pink roses / Total number of roses

Fraction of pink roses = 7 / 12

Therefore, the fraction of the bouquet that is pink roses is 7/12.

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Answer:

the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

Step-by-step explanation:

The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]

The parent function is f(x)=x^2

Now we compare parent function f(x) and g(x)

In g(x), negative sign at first

f(x) ----> -f(x) , the graph is reflected across x axis

f(x)-----> f(x-h), the graph will be transformed h units to right

f(x)----> f(x) +k , the graph will be transformed k units up

[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

Answer:

[tex]\frac{72}{4}=18[/tex]

Step-by-step explanation:

To find : What is a distributive property of 72 divided by 4 ?

Solution :

The distributive property of division is given by,

[tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]

We have to divide 72 by 4,

So, Re-write 72 as 60+12.

Substitute,

[tex]\frac{72}{4}=\frac{60+12}{4}[/tex]

[tex]\frac{72}{4}=\frac{60}{4}+\frac{12}{4}[/tex]

[tex]\frac{72}{4}=15+3[/tex]

[tex]\frac{72}{4}=18[/tex]

Therefore, [tex]\frac{72}{4}=18[/tex]

While the distributive property is typically relevant for multiplication over addition or subtraction, you can apply it to division by first rewriting the division as multiplication by the reciprocal. For example, 72 divided by 4 can be rewritten as 72 times 1/4, and then distributed over a sum or difference.

The distributive property involves multiplication and addition or subtraction, not division. However, if we interpret your question in a bit different way, we can make use of the distributive property for division. To start, dividing 72 by 4 is the same as multiplying 72 by 1/4. So, we can rewrite it as follows:

72 * 1/4

The distributive property is applied when you multiply a number by a sum or a difference. For example, in case of [tex]72*1/4 = (40+32)*1/4[/tex], it would distribute as: [tex]40*1/4 + 32*1/4[/tex]. It gives us 10 + 8 = 18 which is the correct answer. This way, the distributive property can be used in division if the division is expressed as a multiplication.

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y = something x plus or minus a number

going through each line it isn't a linear pattern ( they don't all have the same difference when subtracted or added together)

so now you play around with quadratic equations ( square roots, powers, etc.)

 and you will see that y = x^2 -5

Final answer:

To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.

Explanation:

In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.

To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.

Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.

Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:

 m = P[r(1+r)^n] / [(1+r)^n-1]
Where:

Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.

After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.