A bookcase is to have 4 shelves including the top as pictured below.

The width is to be 16 feet less than 4 times the height. Find the width and the height if the carpenter expects to use 26 feet of lumber to make it.

Answer:

Sara's speed was 6.4 meters per second faster

Step-by-step explanation:

(Were going to name the olympian steve)

First, we have to find how many meters per second Steve ran. To find this we must divide the number of meters he ran by the amount of time it took him to run all 100 meters.

100 ÷ 9.6 =10.41666667

Since the problem tells us to round to the nearest tenth of a second we round 10.41666667 to 10.4. So now we know how many meters per second Steve ran. Now all we have to do is subtract the number of meters per second Sarah ran, from the number of meters per second Steve ran.

Sarah- 16.8 meters per second

Steve- 10.4 meters per second

16.8-10.4= 6.4

And there you have it! Sarah ran 6.4 meters per second more than Steve. I hope this answer was accurate and helpful. I hope you have an AMAZING day!

Answer:

C

Step-by-step explanation:

Answer:

-6.8

Step-by-step explanation:

When your going up you add a number.

Answer:

Hey there!

(8^2)^-4=8^2(-4), or 8^-8

8^-8 can be expressed as the third option.

Hope this helps :)

Answer:

What?

Step-by-step explanation:

Answer:

600 tangerines in total

Step-by-step explanation:

If I am reading it correctly, Desmond purchased 5 boxes, and Molly purchased 5 boxes, meaning that would be 10 boxes in total. 10 times 60 is 600.

Answer:

2 1/2 miles per hour

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The set with 4 elements are listened, a,b,c,d

the set that is given is A, b, c.

Answer:

0.6384

Step-by-step explanation:

Given that:

10-mg Atorvastatin Placebo Headache  15      65       No headache 17      3

Hence the total of number of patients = 15 + 65 + 17 + 3 = 100 patients

The number of patients with headache = 15 + 65 = 80 patients

Also, C(n, x) is the number of combinations in which n items can be chosen taken x at a time it is given by the formula:

[tex]C(n,x)=\frac{n!}{(n-x)!x!}[/tex]

The the probability that if two different subjects they both had a headache = [tex]\frac{C(80,2)}{C(100,2)}=\frac{\frac{80!}{(80-2)!2!} }{\frac{100!}{(100-2)!2!} } =\frac{3160}{4950}=0.6384[/tex]

Complementary angles are two angles which sum is equal to 90 degrees

angle DFG and angle JKL are complementary angles

DFG = x + 3

JKL = x - 5

x-5 +x + 3 = 90

Add like terms

2x - 2 = 90

Add 2 to each side

2x = 92

Divide each side by 2

x = 46

Let's plug 46 into x for angle DFG

46 + 3 = 49

Since they add up to 90, we can subtract 49 from 90 to get angle JKL

90 - 49 = 41

DFG = 49

JKL = 41

For question 5, bisecting means cutting something in half. Angles LMO and NMO are equal to each other.

6x - 21 = 2x + 31

Let's subtract 2x from both sides and add 21 to both sides

4x = 52

Divide each side by 4

x = 13

Let's plug 13 in for x

LMO = 6(13) - 21 = 57

Since LMO and NMO are equal, we can multiply 57 by 2

57 * 2 = 114

The measure of LMN is 114

Answer:

360

Step-by-step explanation:

If x is gallons of 70% antifreeze solution, then:

0.70x + 0.20(90) = 0.60(x + 90)

0.70x + 18 = 0.60x + 54

0.10x = 36

x = 360

Answer:

Amy-24

Barry-21

Clarence-17

Step-by-step explanation:

Clarence is the youngest and so you add 4 to that to get Barry, add 3 more to that to get Amy.

Answer:

basically u have to beble gep

Step-by-step explanation:

art

I'll do problem 5 to get you started.

The reason why choice B is one answer is because we have something in the form y = k/x to indicate an inverse variation. Replace x with H and y with T, and you'll get the same basic equation.

With inverse variation equations, as one variable goes down, the other variable goes up. Think of a see-saw as one way to visualize what's going on.

Or you can think of the T as T/1. So the equation T = L/H is the same as T/1 = L/H. If H were to decrease, then T would increase, and vice versa. T and H are on opposite sides of their respective fractions which may help see this opposite moving nature of each variable.

The reason why choice D is also an answer is because we can multiply both sides of T = L/H by H to get HT = L or TH = L. The equations T = L/H and TH = L are equivalent equations.

Answer:

5. 2nd and 4th boxes

Step-by-step explanation:

These look like proportionality questions. Typically we hear about two main types of proportionalities:

Directly proportional variables are, intuitively, on opposite sides of an equation and both in the numerator on their side. Inversely proportional variables are on opposite sides but with one in the numerator and one in the denominator.

I can't see what the top one is asking for nor the bottom of 6., but let me try and use 5. as an example. If H increases as T decreases, then the two are inversely proportional. So the form would either have to be H=1/T or T=1/H. Other variables can be thrown into the mix and not change the outcome, so the 2nd and 4th boxes are your answers for 5.

Answer:

x > -17/2

Step-by-step explanation:

Step 1: Write inequality

-2x - 5 < 12

Step 2: Solve for x

Add 5 to both sides: -2x < 17

Divide both sides by -2: x > -17/2

Here, we can see that any number greater than -17/2 would work, so x could equal 01234718905731857013570 if we wanted it to, as long as it is greater than -8.5.

Answer:

C. 400

Step-by-step explanation:

Subtract 600 by 200, and get your answer.

Answer:

C

Step-by-step explanation:

600-200=400 that's your answer

Answer:

The cost must be $32 since that is the only cost possible for the 1st deal  

Step-by-step explanation:

Let C represent the total cost of each deal  

Let T be the number of trips down the water slide

C = 32        for the 1st deal since the cost is the same regardless of how much she rides  

C = 18 + T  for the 2nd deal

To find when the two costs are equal set them equal to each other and solve for T

32 = 18 + T

T = 14  trips

The cost must be $32 since that is the only cost possible for the 1st deal  

Answer:

Yes

Step-by-step explanation:

-0.347 is a rational number because all positive and negative numbers are integers

Answer:

0

Step-by-step explanation:

It’s easy

Answer:

Error or Undefined

(12x^2 - 15x) / 3x

Divide the expression by 3x

4x - 5 is the simplified version of your expression

Answer: Choice A) [tex]x > -3[/tex]

There's an open hole at -3 and shading to the right of this hole.

The hole indicates "do not include this endpoint". So we won't have an "or equal to" as part of the inequality sign.

The shading is to the right meaning we are shading everything larger than -3.

Answer:

0.006

Step-by-step explanation:

The probability that the first card is a six is 4/52.

There's one less card now, so the probability that the second card is nine is 4/51.

The total probability is:

P = (4/52) (4/51)

P ≈ 0.006

If Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a six and then selecting a nine.  The probability of selecting a six and then selecting a nine is 0.006

Let the probability that the first card is six be 4/52

Let the probability that the second card is nine be 4/51

Now let determine the probability of selecting a six and then selecting a nine

Probability (P)=(4/52×4/51)

Probability (P)=16÷2,652

Probability (P)= 0.006

Inconclusion if Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a six and then selecting a nine.  The probability of selecting a six and then selecting a nine is 0.006

Learn more here:

https://brainly.com/question/18141369

Answer:

I would say

Step-by-step explanation:

303030 divided by 666 =455

666x455=303030

455-666=2110

so it would be 2110

Answer:

Step-by-step explanation:

7>4n=6 or 7>4+n=6

Answer:

[tex]\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]

Step-by-step explanation:

Given that:

The surface area (S.A) [tex]z = x^2 +y^2[/tex]

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

[tex]A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA[/tex]

where :

D = cylinder [tex]x^2 +y^2 =1[/tex]

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, [tex]\dfrac{\partial z}{\partial x} = 2x[/tex] and [tex]\dfrac{\partial z}{\partial y} = 2y[/tex]

Therefore;

[tex]S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA[/tex]

[tex]= \iint_D \sqrt{1+4(x^2+y^2)} \ dA[/tex]

[tex]= \int^{2 \pi}_{0} \int^{1}_{0} \sqrt{1+4r^2} \ r \ dr \d \theta[/tex]

[tex]= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0[/tex]

[tex]= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1][/tex]

[tex]\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]

Answer:

63.64%

Step-by-step explanation:

Let P(M) be the percentage of students enrolled in a mathematics course

Let P(C) be the percentage of students enrolled in a Computer Science (CS) course.

We are told that One-fifth of those taking a mathematics course arealso taking a computer science course.

Thus, we can write that as:

P(M|C) = 1/5,

We are also told that one-seventh of those taking a computer science course are also taking a mathematics course.

Thus, we can write it as;

P(C|M) = 1/7

According to sets notations, P(M ∩ C) will be the probability that any student is enrolled in both Maths and Computer Science.

Thus;

P(M ∩ C) = P(M|C)P(C) = (1/5)P(C)

Also,

P(M ∩ C) = P(C|M)P(M) = (1/7)P(M)

Equating them, we have;

(1/5)P(C) = (1/7)P(M)

P(C) = (5/7)P(M)

Now; P(M U C) = 1

Let's express out P(M U C)

P(M U C) = P(M) + P(C) - P(M ∩ C) = P(M) + (5/7)P(M) - (1/7)P(M) = (11/7)P(M)

1 = (11/7)P(M)

P(M) = 7/11 = 0.6364 or 63.64%

Answer:

3/8÷2/5=3/8×5/2=15/16

Step-by-step explanation:

When dividing by fractions, invert and multiply.

3/8÷2/5=3/8×5/2=15/16

Answer:

5x feet

Step-by-step explanation:

it is 5x because you got to take away the x and just add them together then and the x to the soultion you get

Answer:

4

Step-by-step explanation: