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Answer:

The diagonal is 39.54 in

Step-by-step explanation:

First we use the Pythagorean theorem to calculate the length of the diagonal of the base.

If the base measures 13 inches by 35 inches then the diagonal is:

[tex]c = \sqrt{13^2 +35^2}\\\\c= 37.34\ in[/tex]

Now we use the Pythagorean theorem again to find the diagonal of the cube.

If the height of the box is 13 inches and the diagonal of the base is 37.34 inches then the diagonal of the cube will be

[tex]z = \sqrt{37.34^2 +13^2}\\\\z= 39.54\ in[/tex]

The baton will fit in the box if it is placed in the direction of the diagonal of the cube, since:

39.54\ in > 38 inches

Using the 3D Pythagorean theorem, the diagonal of the box is calculated to be approximately 39.53 inches, which means that Kylie's 38-inch baton will fit inside the box diagonally.

Kylie needs to check if her 38-inch long baton will fit diagonally in a box with dimensions of 13 inches by 35 inches by 13 inches. To determine whether the baton will fit, she needs to find the length of the longest diagonal of the box. This is solved by using the 3D Pythagorean theorem, which is an extension of the traditional Pythagorean theorem applied to three dimensions.

To find the length of the diagonal (d), we use the formula:

d = √(l² + w² + h²)

Where l is the length, w is the width, and h is the height of the box. Substituting the given values:

d = √(13² + 35² + 13²)

d = √(169 + 1225 + 169)

d = √1563

d ≈ 39.53 inches

The calculated diagonal length of approximately 39.53 inches indicates that Kylie's baton, which measures 38 inches, will indeed fit inside the box diagonally.

Answer:

The money was invested for 16 years

Step-by-step explanation:

This is a compound interest problem and the following information has been provided;

Principal, P = 2500

Rate, r = 0.05 compounded semiannually. This will imply an effective rate of 0.05/2 = 0.025 effective per semiannual period.

Accumulated amount, A = 5509.39

We are required to determine the duration of investment in years. We let the number of years be n. We then use the compound interest formula;

[tex]A=P(1+r)^{n}\\\\5509.39=2500(1+0.025)^{2n}[/tex]

We raise to power 2n since there are 2n semiannual periods in n years. The next step is to divide both sides by 2500;

[tex]2.203756=1.025^{2n}\\[/tex]

We introduce logs in order to solve for n;

[tex]ln(2.203756)=2nln(1.025)\\\\2n=\frac{ln(2.203756)}{ln(1.025)}\\ \\2n=32\\\\n=16[/tex]

Answer:

p = 2 , q = 0

Step-by-step explanation:

Solve the following system:

{-28 = -14 p - 40 q | (equation 1)

10 q + 4 = 2 p | (equation 2)

Express the system in standard form:

{14 p + 40 q = 28 | (equation 1)

-(2 p) + 10 q = -4 | (equation 2)

Add 1/7 × (equation 1) to equation 2:

{14 p + 40 q = 28 | (equation 1)

0 p+(110 q)/7 = 0 | (equation 2)

Divide equation 1 by 2:

{7 p + 20 q = 14 | (equation 1)

0 p+(110 q)/7 = 0 | (equation 2)

Multiply equation 2 by 7/110:

{7 p + 20 q = 14 | (equation 1)

0 p+q = 0 | (equation 2)

Subtract 20 × (equation 2) from equation 1:

{7 p+0 q = 14 | (equation 1)

0 p+q = 0 | (equation 2)

Divide equation 1 by 7:

{p+0 q = 2 | (equation 1)

0 p+q = 0 | (equation 2)

Collect results:

Answer:  {p = 2 , q = 0

Answer:

p = 2 , q = 0

Step-by-step explanation:

Trust me

Answer: C.

Step-by-step explanation:

Diameter = Radius/2

So, the radius would be 6.5 in.

The formula for the volume of a sphere is: V = 4/3 (3.14) r^3.

So, once you "plug in" the radius, you get an equation of V = 4/3 (3.14) r^3.

And, once you solve the equation, you get and answer of 1,150 in.^3, rounded to the nearest cubic inch.

The volume of a sphere with a diameter of 13 inches, using the formula V = 4/3 * π * r³ and rounding off to the nearest cubic inch, is approximately 1151 cubic inches or choice C, 1150 in³.

To find the volume of a sphere, you can use the formula V = 4/3 * π * r³, where V is the volume and r is the radius. In this case, the diameter of the sphere is given as 13 inches. So, the radius would be half the diameter, which is 6.5 inches.

Plugging the values into the formula, we get V = 4/3 * 3.14 * (6.5)³. Calculating this gives an approximate value of 1151 cubic inches. Since we need to round to the nearest cubic inch, the final volume is 1151 in³.

So, the correct choice is C. 1150 in³.

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Answer:

20% it would be 10% if there was 10 items. 5 items mean every item has 20%.

Step-by-step explanation:

Answer:  0.20

Step-by-step explanation:

Given : The number of side dishes for the lunch menu =6

The number of ways to select 3 dishes from 6 :

Total outcomes : [tex]^6C_3=\dfrac{6!}{3!(6-3!)} \ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}\ ][/tex]                  

If applesauce and broccoli is already selected , then we need to select only one dish out of remaining 4 dishes.

Number of ways to select 1 dish from 4 :

Favorable outcomes: [tex]^4C_1=\dfrac{4!}{1!(4-1)!)}=4[/tex]

Now, the theoretical probability that applesauce and broccoli will both be offered on Monday :-

[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{4}{20}=0.20[/tex]

Hence, the theoretical probability that applesauce and broccoli will both be offered on Monday = 0.20

Answer:

Option B.

Step-by-step explanation:

The constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

Given that the graph is a straight line, we can find the constant of proporctionality just by selecting a point, and then dividing the y-value by the x-value.

We can see from the graph that when y=5, x=4. Then, the constant of proportionality comes to be:

k = 5/4 = 1.25.

Then, the correct option is Option B.

The expression (4y^6)^3 - (10z^2)^3 is equivalent to 64y^18 - 1000z^6.

Factor out common powers:

64y^18 = (2^6)(y^3)^6

1000z^6 = (10^3)(z^2)^3

Rewrite the expression with factored terms:

64y^18 - 1000z^6 = (2^6)(y^3)^6 - (10^3)(z^2)^3

Apply power of a power rule:

(a^m)^n = a^(mn)

(2^6)(y^3)^6 = 2^(66) * y^(36) = 2^36 * y^18

(10^3)(z^2)^3 = 10^(33) * z^(2*3) = 10^9 * z^6

Substitute back the simplified terms:

2^36 * y^18 - 10^9 * z^6 = (4y^6)^3 - (10z^2)^3

Therefore, (4y^6)^3 - (10z^2)^3 is the equivalent expression to 64y^18 - 1000z^6. Both expressions involve the difference of cubes of binomials, with one focusing on powers of 4y^6 and the other emphasizing powers of 10z^2.

Answer:Vertical Asymptotes: x=0

Horizontal Asymptotes: y=2

Here’s a graph picture...

The answer is y = 3x - 2

Y=3x-2

The formula y=mx+b is the slope intercept formula. You would enter the information of the problem into the equation.

You would place the slope in the place of m and the y intercept in the place of b.

Since it is a negative slope it would be -2 instead of +2 if it was positive.

Answer:

Step-by-step explanation:

First step:

Calculate the hypotenuse of a right triangle.

Use the Pythagorean theorem:

[tex]h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\\\\h=5\ cm[/tex]

Second step:

We have

two right triangles with legs a = 3cm and b = 4 cm

one rectangle 4cm × 2cm

one rectangle 3cm × 2cm

one rectangle 5cm × 2cm

Calculate each area:

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

Substitute:

[tex]A_1=\dfrac{(3)(4)}{2}=(3)(2)=6\ cm^2[/tex]

The formula of an area of a rectangle l × w:

[tex]A=lw[/tex]

Substitute:

[tex]A_2=(4)(2)=8\ cm^2\\\\A_3=(3)(2)=6\ cm^2\\\\A_4=(5)(2)=10\ cm^2[/tex]

Third step:

Calculate the Surface Area of the figure:

[tex]S.A.=2A_1+A_2+A_3+A_4[/tex]

Substitute:

[tex]S.A.=2(6)+8+6+10=36\ cm^2[/tex]

The line in the middle has a right angle, so the angle just above the Y would be 90 degrees.

The angle to the right of y is given as 48.

The three inside angles of a triangle need to equal 180.

So y  = 180 - 90 - 48 = 42 degrees.

Answer:

High positive correlation

Step-by-step explanation:

Perfect correlation is 1 or -1(0 is no correlation), the correlation coefficient is .8

It is positive because it is a positive number (closest to positive 1).

This value is close to 1 so it's a high positive correlation.

Answer:

Answer Is C.

Step-by-step explanation:

Answer:

900 miles

Step-by-step explanation:

Well, 200 miles is 1 inch. 100 miles is 1/2 an inch.

Answer:

900

Step-by-step explanation:

Given: 1/4 in. = 50 miles

Find the amount of miles per inch. Multiply 4 to both sides of the equation.

(1/4 in.) x (4) = (50 miles) x (4)

4/4 in. = 200 miles

1 in. = 200 miles

Now, find the amount of miles for 4 1/2 in. Multiply 4 1/2 to both sides.

Note that 4 1/2 = 4.5

(1 in.)(4.5) = (200 miles) x (4.5)

4.5 = 200 x 4.5

4.5 = 900

900 miles is your answer.

~

Answer:

295

Step-by-step explanation:

.3 x 295 = 88.5

295 - 88.5 = 206.5

Answer:It will be 2/12

Step-by-step explanation:

6 blue chips           6 red chips

6+6=12  so 2 red chips to 12 =2/12

Answer:

(1+10)+18=11+18=29; 1+(10+18)=1+28=29

Step-by-step explanation:

the associative property of addition means that no matter in what order you group the numbers for addition the results come out to be the same.

using the associative property of addition to find the total of 1,10, and 18 in two different ways

first: (1+10)+18

=11+18

=29

second: 1+(10+18)

=1+28

=29!

Answer:

Choice B: BD/DA = CE/EA

Step-by-step explanation:

Slope is rise over run. For the two slopes to be equal, the rise over run of the two triangles must be equal.

The rise over run for triangle ABD is BD/DA.

The rise over run of triangle ACE is CE/EA.

For the slopes to be equal, BD/DA = CE/EA

Answer: Choice B.

Answer:

4.5

Step-by-step explanation:

because 2 3 4 4 5 7 9 11

4.5 is the middle number, between 4 and 5 since you find what the middle number is

Here is some fun:

[tex]mean=\frac{\Sigma_{0}^{n}a_r}{n}=\frac{a_0+a_1+\dots+a_{\infty}}{\infty}[/tex]

[tex]

mean=\frac{4+5+9+2+7+4+3+11}{8}=\frac{45}{8}=\boxed{5.625}

[/tex]

And now the real work:

[tex]median=\frac{2+7}{2}=\boxed{4.5}[/tex]

The answer is B. 4,5

Hope this helps.

r3t40

c increased by 17

Increased = +

c + 17 is the answer

Answer:

Error question or wrong

Multiply the numbers by 2

7*2=14

14*2= 28

28*2=56

Answer is 56

ANSWER

56

EXPLANATION

We want to find the next number in the sequence,

7,14,28,

Observe that, there is a common ratio of 2 among the terms.

That is ,

7(2)=14

14(2)=28

Therefore the next term is

28(2)=56

Therefore the number that goes into the box is 56.

Answer:

y - 4 = -1/2(x+6).

Step-by-step explanation:

The equation of the line is: y - y0 = m(x-x0)

If the line passes through the points (x1, y1)=(-6, 4) and (x1, y1)=(2, 0). Then, the slope is:

[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-4}{2-(-6)} = -\frac{1}{2} [/tex]

Then, the equation is: y - 4 = -1/2(x+6).

$22.75

Start by finding the cost of each topping. Subtract $17.50 minus $14.00 to find that adding 2 toppings costs $3.50. Now, divide $3.50 by 2 to find that the cost for adding only one topping is $1.75.

Then, multiply $1.75 by 5 to find how much it costs to add 5 toppings. You get $8.75.

Finally, add the cost of 5 toppings to the cost of a large pizza with no toppings. $14.00 plus $8.75 equals $22.75, so a large pizza with 5 toppings costs $22.75.

Answer: $22.75

Step-by-step explanation:

Given : The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function.

A linear function is given by :-

[tex]y=mx+c[/tex]                            (1)

, where m is slope (rate of change of y w.r.t x) and c is the y-intercept.

A large pizza with no toppings costs $14.00.

i.e. for x=0 , y= 14

Put theses values in (1) , we get

[tex]14=m(0)+c\\\Rightarrow\ c=14[/tex]   (2)

A large pizza with 2 toppings costs $17.50.

i.e. for x=2 , y= 17.50

Put theses values in (1) , we get

[tex]17.50=m(2)+c[/tex]      

Put value of c from (2)

[tex]17.50=2m+14\\\\[/tex]      

Subtract 14 from both sides , we get

[tex]3.50=2m[/tex]

Divide both sides by 2 , we get

[tex]1.75=m[/tex]

Put m= 1.75 and c= 14 in (1) , the linear function representing cost of large pizza becomes [tex]y=1.75x+14[/tex]

At x= 5

[tex]y=1.75(5)+14=8.75+14=22.75[/tex]

Thus , the cost of a pizza with 5 toppings= $22.75

Answer:

[tex]x=6\sqrt{5}\\ \\y=3\sqrt{5}\\ \\z=6[/tex]

Step-by-step explanation:

The height of the right triangle drawn to the hypotenuse is geometric mean of two segments of hypotenuse, so

[tex]z^2=12\cdot 3\\ \\z^2=36\\ \\z=6[/tex]

By the Pythagorean theorem,

[tex]x^2=12^2+z^2\\ \\x^2=144+6^2\\ \\x^2=144+36\\ \\x^2=180\\ \\x=6\sqrt{5}[/tex]

and

[tex]y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3\sqrt{5}[/tex]

Answer:

D

Step-by-step explanation:

Since the denominators of both fractions are common, then subtract the numerators leaving the common denominator, that is

[tex]\frac{4a+1-2a-7}{a^2-4}[/tex] = [tex]\frac{2a-6}{a^2-4}[/tex]

Answer:

[tex]\boxed{\bold{\frac{2a-6}{a^2-4}}}[/tex]

Explanation:

Apply Rule [tex]\bold{\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}[/tex]

= [tex]\bold{\frac{4a+1-\left(2a+7\right)}{a^2-4}}[/tex]

Expand [tex]\bold{4a+1-\left(2a+7\right): \ 2a-6}[/tex]

= [tex]\bold{\frac{2a-6}{a^2-4}}[/tex]

Mordancy.

Answer:

C. 3Pi/2 or 270 degrees

Step-by-step explanation:

The first step is to ignore the negative sign and then evaluate the arcsin of 1 to obtain the reference angle of θ in the first quadrant;

θ = arcsin(1)

θ = 90 degrees or equivalently pi/2

Since the sine of θ was given as -1, this will imply that θ lies either in the third or forth quadrant where the sine of an angle is negative.

To obtain the value of θ in the third quadrant we simply add 180 degrees of pi radians to our reference angle;

90 + 180 = 270 degrees

pi/2 + pi = 3/2 pi

I hope I'm not wrong here, but B.1/2? Only because its a 50% chance

The fraction of the time will you expect to see a head on the sixth flip will be 1/2.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Here the sample variables are = [3 heads , 2 tails]

The number of the times coin flipped = 6 times

Probability of the flipping the coin and having head will be

P(A)=3/6=1/2

Hence the fraction of the time will you expect to see a head on the sixth flip will be 1/2.

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Answer:

x = - 2, x = 12

Step-by-step explanation:

Given

x² - 10 x  = 24 ( subtract 24 from both sides )

x² - 10x - 24 = 0 ← in standard form

To factorise the quadratic

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 10)

The factors are - 12 and + 2, since

- 12 × 2 = - 24 and - 12 + 2 = - 10, thus

(x - 12)(x + 2) = 0

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

x + 2 = 0 ⇒ x = - 2

The solution of this quadratic equation to x² – 10 x = 24 is  x = - 2 & x = 12

A quadratic is a sort of problem that deals with a variable accelerated by using an operation called squaring. This language derives from the area of a rectangular being its facet period expanded with the aid of itself. The phrase "quadratic" comes from quadrant, the Latin word for square.

x² – 10 x = 24

⇒ x² +2X -12X -24 = 0

⇒ x (x - 2) -12(x - 2) =0

⇒ x = 12 OR ( x = -2)

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Answer:

n = 4

Step-by-step explanation:

Given

10n + 2 = 7n + 14

Collect terms in n on the left side and numbers on the right side

Subtract 7n from both sides

3n + 2 = 14 ( subtract 2 from both sides )

3n = 12 ( divide both sides by 3 )

n = 4

Answer n=4

Step-by-step explanation: Collect the like terms 10n-7n=14-2

3n=12 divide both sides by 3

-10t+6=-44

-10t=-50

t= 5

ANSWER

[tex]h(5) = - 44[/tex]

EXPLANATION

The given expression is :

h(t)=-10t+6

We want to find the value of t that will evaluate to -44.

We equate the function to -44 and solve for t.

[tex]-10t+6 = - 44[/tex]

Subtract 6 from both sides of the equation,

[tex]-10t = - 44 - 6[/tex]

[tex]-10t = - 50[/tex]

Divide both sides by -10

[tex]t = 5[/tex]