A box is 30 inches wide, 16 inches long, and 14 inches high. To the nearest cubic inch, what is the volume of the box?

Answer:

1 year

Step-by-step explanation:

Hello,

Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).

[tex]\displaystyle e^{(1+4.5\%)t}=e^{\left( 1.045\cdot t \right) }[/tex]

So we need to find t so that:

[tex]\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...[/tex]

Rounding to the nearest whole number gives 1 year.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

25

Step-by-step explanation:

Trust me

Answer:

x=

a.60

b.25

c.45

d.30

e.53

f.is a right angle so 90

g.15

h.is a right angle so 90.we have to divide it so it's 45.equal to both sides.

Step-by-step explanation:

by looking at the angles we know

first one is 180.so simply just subtract from the number given.like that we do..

as you can see H ,there the symbol means both sides are equal so the amount will be same.

it was all about equating some values

to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Let's determine the number of cooks required to bake the required number of cakes during the available time.

We have the following information:

- Each cook can bake either 5 large cakes or 14 small cakes per hour.

- The kitchen is available for 3 hours.

- We need to bake 29 large cakes and 260 cakes in total.

First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:

1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.

Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:

1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.

Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:

Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours

We need to bake 29 large cakes, so:

29 = Number of cooks × 15

Number of cooks = 29 / 15 ≈ 1.93

Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.

Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:

Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours

We need to bake 260 small cakes, so:

260 = Number of cooks × 42

Number of cooks = 260 / 42 ≈ 6.19

Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.

Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.

Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

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Answer:

The side opposite <Q is RS

The hypothenuse is QR

The side adjacent to <Q is QS

Step-by-step explanation:

Side RS is directly opposite <Q. The first statement provided in the options is correct.

The side that is opposite to <R is QS. The second statement in the options is not correct.

The longer leg of a right triangle is always the hypotenuse. Side QR in ∆QRS is the hypotenuse. The third statement given in the options is correct.

The side adjacent to <R is not SQ. RS is the side adjacent to <R. The fourth statement in the given options is not correct.

Side QS is adjacent to <Q. The fifth option is correct.

Answer:

A, C, E

Step-by-step explanation:

on edge! hope this helps!!~ （‐＾▽＾‐）

if. 25 miles : 1 gallon

300 miles. : ?

if more less divides

300/25×1

=12 gallons of gas will be used

Answer:18 ft

Step-by-step explanation: Perimeter=2(L+B)

Perimeter=2(7 + 2)

2×9=18

Answer:

18feet.

Step-by-step explanation:

To find the perimemter of a rectangle, you just add all the sides.

A rectangle has 4 sides in total, where 2 are equal, and the other 2 are als equal.

So, you just add 7+2+7+2, which gives 18.

This is why, the perimeter of this rectangle is 18feet.

Hope this helped, have a nice day!

Answer:

The answer is

[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]

Step-by-step explanation:

Since the Earth's moon is a sphere

Surface area of a sphere from the question is given by

A = 4πr²

where r is the radius

To find the radius using the diameter we use the formula

radius = diameter / 2

[tex]radius \: = \frac{3.8 \times {10}^{8} }{2} [/tex]

[tex]radius = 1.9 \times {10}^{8} \: m[/tex]

π = 3.14

Substitute these values into the above formula

That's

[tex]A = 4 \times 3.14 \times ({1.9 \times {10}^{8} })^{2} [/tex]

We have the final answer as

[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]

Hope this helps you

Question options :

A. There is sufficient evidence to reject the claim

u < 99.

B. There is sufficient evidence to support the claim

u < 99.

C. There is not sufficient evidence to reject the claim

u < 99.

D. There is not sufficient evidence to support the claim

u< 99.

Answer:

B. There is sufficient evidence to support the claim

u < 99.

Step-by-step explanation:

We construct the n*ll and alternative hypotheses to support our claim

The n*ll hypothesis :H0

The alternative hypothesis : Ha

N*ll hypothesis =H0: u=99

Alternative hypothesis =Ha: u<99

So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99

we can therefore have sufficient evidence to support our claim that u<99

Answer:

y= -4/3x+10 2/3

Step-by-step explanation:

To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.

I hope my explanation wasn't confusing and that my answer helped.

Answer:

52 cups

Step-by-step explanation:

1 gallon = 4 quarts

1.5 gallons = 6 quarts

6 + 9 = 13 quarts of lemonade in the fridge.

1 quart = 4 cups

13 quarts = 4 × 13 = 52 cups

52 cups of lemonade are in the fridge.

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Answer:

60 cups

Step-by-step explanation:

1 gal = 16 cups

1 quart = 4 cups

               16 cups

1.5 gal x ------------- = 24 cups

                  1 gal.

                 4 cups

9 quarts x ----------- = 36 cups

                  1 quart

number of cups of lemonade in the fridge = 24 cups + 36 cups = 60 cups

Answer:

The "square root spiral," donned the "Spiral of Theodorus" was created by Theodorus to visualize a set of 17 isosceles triangles where [tex]n[/tex] is equal to a value between one and seventeen.

I have attached an image of the Square Root spiral below.

Answer:

Step-by-step explanation:

Given the limit of the function [tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }[/tex]

First step is to substitute the given values of x, y and z into the function given as shown;

[tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }\\\\= e^{-(7)(0)}sin\dfrac{\pi (2)}{4} }\\\\\\= e^{-0}sin\dfrac{\pi}{2} }\\\\\\= 1*sin\frac{\pi}{2} \\\\= 1*sin90^0\\\\= 1* 0\\\\= 0[/tex]

The limit therefore exist since the limit of the function at the given point gave us a finite value which is zero.

Answer:

For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value

Step-by-step explanation:

Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.

Mathematically, the null hypothesis is as expressed as below;

H0: μ = 1,200

The alternative hypothesis H1 would be;

H1: μ > 1,200

Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics

For us to reject the null hypothesis, one of two things, or two things must have occurred.

The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.

If this happens, then we can make a rejection of the null hypothesis

Answer:

Because it increases the risk of Type 1 error

Step-by-step explanation:

ANOVA is the analysis of the variance .

When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error  .

For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.

This has two disadvantages .

First the procedure is too lengthy  and tediuos.

Second the overall level of significance greatly increases as the number of t- tests increases.

The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.

Answer:

Hey there!

Simple interest formula: I=PRT

I=700(8.25)(0.25)

I=1443.75

Hope this helps :)

Answer:

Step-by-step explanation:

I = PRT

I = 700(0.0825)(1/4) = 14.44

Because the interest is usually in percentage and it's impossible to have 825% as your interest rate. So the actual interest rate has to be 0.0825.

The formula above calculated the interest, if you want the total, you will need to add 700 to that number.  

Here's a small quick example of the formula that should help.

Answer:

x+10 =2

x = -8

Step-by-step explanation:

plus means add

x+10 =2

Subtract 10 from each side

x+10-10 =2-10

x = -8

I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.

The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.

Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]

The y  intercept 3.787 represents the  height of that is independent of Arm span.

The height of the person whose arm span is 66 inches is 66.817 inch.

The arm span of a person whose height is 74 inches is 73.52 inch

According to the given data the arm span  and heights are given in inches

Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis

The  image for the excel work done showing calculations and scatter plot  is attached.

Now we can fit the linear tread line and  to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]

Slope of line of best fit = 0.955

So we can conclude that height (Y) is related to Arm span according to equation (1)

Equation (1) shows the equation of line of best fit for the given data

The y  intercept 3.787 represents the  height of that is independent of Arm span.

So the height of the person whose arm span is 66 inches is given following

[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]

Similarly the arm span of a person whose height is 74 inches

[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]

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Answer:

the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.

Step-by-step explanation:

Answer:

The probability is  [tex]P(2) = 0.426[/tex]

Step-by-step explanation:

From the question we are told that

         The probability of  success is [tex]p = 0.26[/tex]

          The number of hits is  n =  7

Generally this probability follows a binomial distribution given there can only be two outcome i.e the probability of success and the probability of failure

       The probability of failure is  [tex]q = 1- p[/tex]

substituting values

               [tex]q = 1 - 0.26[/tex]

               [tex]q = 0.74[/tex]

Now the probability of  exactly 2 hits in his next 7 at bats is mathematically evaluated as

     [tex]P(2) = \left n} \atop {}} \right. C_2 *p^{2} * q^{n- 2}[/tex]

substituting values

    [tex]P(2) = \left 7} \atop {}} \right. C_2 *p^{2} * q^{7- 2}[/tex]

Here [tex]\left 7} \atop {}} \right. C_2[/tex] means 7  combination 2 and using a calculator(reference calculator soup website) to compute, the value obtained is  

          [tex]\left 7} \atop {}} \right. C_2 =21[/tex]

So

     [tex]P(2) = 21 *(0.26)^{2} * (0.74)^{5}[/tex]

     [tex]P(2) = 0.426[/tex]

Answer:

3hours and 12.5 minutes

Step-by-step explanation:

45/6=7.5x25=187.5/60=3hours and 12.5 minutes

Answer:

a. Pr(They both have type O)

= Pr(They both have type O)

= 0.35 x 0.45

= 0.1575 = 15.75%

b. Pr( they both have the same blood type)

= Pr( they both have the same blood type)

= 2/8

= 0.25 = 25%

c. Pr( at least one person has type O)

= Pr (at least one person has type O)

= 1 - 0.3575

= 0.6425 = 64.25%

Step-by-step explanation:

a) Data:

                   O       A         B       AB

Chinese   0.35   0.27    0.26     0.12

American 0.45   0.4      0.11       0.04

b) Calculations:

i. Pr(They both have type O)

= Probability of Chinese with O multiplied by Probability of American with O

= 0.35 * 0.45

= 0.1575 = 15.75%

ii. Pr( they both have the same blood type)

= Probability of two out of 8 outcomes

= 2/8

= 0.25 = 25%

iii. Pr( at least one person has type O)

= Probability of (1 – p(none) )

The probability of none = p(none O blood type)

= p(none)

for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)

= 0.65 * 0.55 = 0.3575

Pr (at least one person has type O) = 1 - 0.3575

= 0.6425

Answer:

$20

Step-by-step explanation:

Company A:

Buy 300 shares at $1.45 per share.

Sell 300 shares at $1.65 per share.

Profit: ($1.65 - $1.45) * 300 = $60

Company B:

Buy 200 shares at $1.20 per share.

Sell 200 shares at $1.10 per share.

Loss: ($1.20 - $1.10) * 200 = $20

Net profit:

$40 - $20 = $20

Answer:

Step-by-step explanation:

Profit on Company A =$(1.65−1.45)×300=$60.

Loss on Company B =$(1.20−1.10)×200=$20.

Therefore the total profit Jamal achieved was $60−$20=$40.

Answer:

Divide the diameter by 2.

Step-by-step explanation:

The radius of any circle is always the end to the center.

The diameter is a point of the circle to the opposite side.

This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.

Hope this helped!

Answer:

Divide the diameter by 2. d/2=r

Step-by-step explanation:

If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.

If the diameter was 10, the radius would 10/2=5.

Answer:

C) 3/2x-1/8

Step-by-step explanation:

We can see that it has a generally positive slope, which rules out B and D.

Plugging in a few numbers for x, we can quickly see that 6 is too high of a slope. (If we plug in 6 for x, the y value would be almost 35, not 10).  This rules out A.

While it doesn’t fit perfectly, C is by far the closest.

Answer:

The percentile that corresponds to an IQ score of 115 is 34.13 %

Step-by-step explanation:

Here, we want to find the percentile that corresponds to an IQ score of 115.

To calculate this percentile, we start with making observations. From the question, we are told that the mean score is 100 while the standard deviation is 15.

Now we want to find the percentile for a score if 115. For a score of 115, we can see that the difference between this score and the mean is 15 which is exactly equal to the standard deviation.

What this means is that the score is within +1 SD of the mean.

For a score of within +1 SD of the mean, the percentile is 34.13%

A score at the mean is the 50th percentile, a score which is 1 SD above or below the mean has a percentile value of 34.13%

Please, I will like you to check the attachment to see how percentiles are valued given the number of standard deviations a particular value is from the mean.

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

Answer:

A. 0,2,0,2

Step-by-step explanation:

Firstly, Insert 1-4 into [tex]u^n=1+(-1)^n[/tex]

[tex]u^1=1+(-1)^1\\1+(-1)1=0\\\\\\\\u^2=1+(-1)^2\\\\1+1=2\\\\\\u^3=1+(-1)^3\\\\1+(-1)^3=0\\\\\\\\u^4=1+(-1)^4\\\\1+(-1)^4=2\\[/tex]

Simple explanation, for the first number.

-1+1=0

For the second number we are saying, -1*-1=1

and then 1+1=2

For the third number we are saying, -1*-1*-1=-1

-1+1=0

For the fourth number we are saying, -1*-1*-1*-1=1

1+1=2

When raising a power inside parentheses to another power, multiply the numbers:

(6^4)^2 = 6^(4x2) = 6^8

Simplified = 6^8

6^8 = 1679616

Answer:

Step-by-step explanation:

[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]

It is the example of Power to power law of indices.

Multiply the exponents

⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]

Multiply the numbers

⇒[tex] \mathsf{ {6}^{8} }[/tex]

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

[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]

If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]

i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.

Hope I helped!

Best regards!!

Hence, the commutative property of addition is not used.

What is an expression?

A mathematical expression is in form of variables and constants separated by their arithmetic operation.

As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],

Distributive property which is [tex]a(b+c) = ab + ac[/tex],

Commutative property which is [tex]a + b = b + a[/tex].

Here given that,

[tex]2 (x+5)+7x=(2x+10)+7x[/tex]      

[tex](2x+10)+7x=(2x+10)+7x[/tex]         ( distributive property of multiplication)

[tex](2x+7x)+10=(2x+7x)+10[/tex]        ( it is associative property of addition)

[tex](8x)+10=(8x)+10[/tex]        ( it is a commutative property)

Hence, the commutative property of addition is not used.

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