A hemispherical bowl of radius 8 inches is filled to a depth of h​ inches, where 0less than or equalshless than or equals8. Find the volume of water in the bowl as a function of h.​ (Check the special cases hequals0 and hequals8​.)

Answer: m=6, m=-4

Step-by-step explanation:

To solve this proportion, we have to cross multiply.

[tex]\frac{m-3}{7} =\frac{m}{m+8}[/tex]

[tex](m-3)(m+8)=7m[/tex]

Now that we have cross multiplied, we actually need to FOIL the left side to expand the equation.

[tex]m^2+8m-3m-24=7m[/tex]

Combine like terms.

[tex]m^2+5m-24=7m[/tex]

We can move all terms to one side and then solve for m.

[tex]m^2-2m-24=0[/tex]

We can actually factor this to:

[tex](m-6)(m+4)=0[/tex]

We set each factor equal to 0 to find m.

m-6=0

m=6

m+4=0

m=-4

Answer:

the vertex of the parabola is at the point; (5, -1)

which agrees with answer "B" in the list of options

Step-by-step explanation:

Notice that this is the equation of a parabola with branches that open horizontally (not vertically), since the variable the goes squared is the y-variable instead of "x".

By analyzing it we can then write it by isolating the term in "x" on one side of the equation, and use at the same time the fact that it is being written in "vertex" form:

[tex]-8\,(x-5)=(y+1)^2\\(x-5)=-\frac{1}{8} (y+1)^2[/tex]

Therefore, the "y-value" of the vertex must be that which renders zero in the expression squared, that is y = -1. On the other hand, the x-value of the vertex is that which renders zero for the variable "x":  x=5.

Then, the vertex of the parabola is at the point; (5, -1)

Answer:

At least 8.96 hours of sleep to be in the top 1%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 7.45, \sigma = 0.65[/tex]

How many hours of sleep to be on the top 1%?

The top 1% is the 100 - 1 = 99th percentile, which is X when Z has a pvalue of 0.99. So X when Z = 2.327. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.327 = \frac{X - 7.45}{0.65}[/tex]

[tex]X - 7.45 = 0.65*2.327[/tex]

[tex]X = 8.96[/tex]

At least 8.96 hours of sleep to be in the top 1%.

Answer:

2.31

.12

7.73

Step-by-step explanation:

σx¯=0.653–√0=0.12

By plugging all the numbers into the formula z=x¯−μσx¯ we find that

2.31=x¯−7.450.12

0.28=x¯−7.45

7.73=x¯

Answer: £500

Step-by-step explanation:

Jules buys the washing machine at £600 including vat

Price before vat

x + 0.2x = 600

1.2x = 600

x = 600/1.2

x = 500

The price of the washing machine with no VAT added would be £500.

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science. Thus, unit price of something is price of 1 thing. Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

WE have given that Jules buys the washing machine at £600 including 20% VAT.

Let x represnt the price of the washing machine with no VAT added.

The Price before vat is;

x + 0.2x = 600

1.2x = 600

x = 600/1.2

x = 500

Therefore, the price of the washing machine with no VAT added would be £500.

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Answer:

Two factor ANOVA

Step-by-step explanation:

They two factor ANOVA is used to determined if there is an interaction between the two independent variables on the dependent variable which in this case study are

The two independent variables are:

One member of each twin pair gets this early discrimination training, but the other does not.

While the dependent variable is their respective IQ scores.

Thus, we can use this test to determine whether the effect of one of the independent variable is the same for all other values of the other independent variable and vice versa using their IQ scores.

Answer:

Step-by-step explanation:

The value of the expression is its distance from zero. The absolute value is the positive value without any minus sign.

  [tex]|-7.1|=7.1\\\\|2.7+4.2|=|6.9|=6.9\\\\|4-9|=|-5|=5\\\\|-3.1+8.8|=|5.7|=5.7[/tex]

Answers:

| -7.1 | — Distance from zero on number line: 7.1

| -3.1 + 8.8 | — Distance from zero on number line: 5.7

| 2.7 + 4.2 | — Distance from zero on number line: 6.9

| 4 - 9 | — Distance from zero on number line: 5

Step-by-step explanation:

Tap the THANKS  button and RATE ⭐️

(If helpful)

Answer:

y = 12

Step-by-step explanation:

If y varies directly as x and z;

y ∝ xz

y = kxz .......1

Where k is the constant of Proportionality;

y=8/3 when x=1 and z=4

Making k the subject of formula and substituting the given values.

k = y/xz

k = (8/3)/(1×4)

k = (8/3)/4

k = 2/3

when x=6 and z=3;

From equation 1;

y = kxz

And;

k = 2/3

x = 6

z = 3

Substituting the values;

y = 2/3 × 6 × 3

y = 12

Answer:

12

Step-by-step explanation:

Answer:

y = -1/5x +32/5

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b

we know m = -1/5

y = -1/5x+b

We know a x and y on the line

7 = -1/5(-3) +b

7 = 3/5 +b

Subtract 3/5 from each side

35/5 -3/5 = b

32/5 =b

So the equation is

y = -1/5x +32/5

Answer:

5.78×10¹⁵

Step-by-step explanation:

The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.

The number of ways he can choose 4 country songs (ignoring the order) is ₂₂C₄ = 7315.

The number of ways he can choose 4 reggae songs (ignoring the order) is ₁₁C₄ = 330.

The number of ways he can choose 4 pop songs (ignoring the order) is ₅C₄ = 5.

The total number of combinations is 7315 × 330 × 5 = 1.21×10⁷.

Once he has his 12 songs selected, the number of ways he can arrange them is ₁₂P₁₂ = 12! = 4.79×10⁸.

So the total number of possible playlists is:

(1.21×10⁷) × (4.79×10⁸) = 5.78×10¹⁵

Answer:

6,4,4,4,5,7

Step-by-step explanation:

Answer: 31-40 6 bracelets, 41-50 4 bracelets, 51-60 4 bracelets, 61-70 4 bracelets, 71-80 5 bracelets, 81-90 7 bracelets

Step-by-step explanation:

6 given numbers within 31-40

4 given numbers within 41-50

4 given numbers within 51-60

4 given numbers within 61-70

5 given numbers within 71-80

7 given numbers within 81-90

Answer:

5 °Celsous

Step-by-step explanation:

-12 + (5 +5+5+5)-3=

-12 + 20 - 3 =

-12 + 17 = 5

Answer:

C

Step-by-step explanation:

i did the test

Answer:

There are 8 sections and 5 of them are less than 7 so the answer is 5/8 = 62.50%.

Answer:

62.5 percent

Step-by-step explanation:

there are a total of 8 options (2,3,4,5,6,7,8,9) the spinner could land on. 5 of these options are less than 7 (6,5,4,3,2)

5/8 is also 62.5 percent

Answer:

(x-4) ^2 + (y+1)^2 = 81    

Step-by-step explanation:

The equation of a circle is given by

(x-h) ^2 + (y-k)^2 = r^2  where (h,k) is the  center and r is the radius

(x-4) ^2 + (y--1)^2 = 9^2

(x-4) ^2 + (y+1)^2 = 81      

Answer:

the set of all possible input values.

Step-by-step explanation:

Answer:

(a)20.65 lbs.

(b)1.88 lbs/month.

Step-by-step explanation:

The median weight of the boy can be approximated by the function:

[tex]w(t)=7.42+1.92t-0.0074t^2+0.000446t^3[/tex]

Where t is measured in months; and

w is measured in pounds.

(a)When the baby is 7 months

Approximate Weight,

[tex]w(7)=7.42+1.92(7)-0.0074(7)^2+0.000446(7)^3\\=20.65$ pounds (to two decimal places)[/tex]

The approximate weight of the baby at age 7 months is 20.65 lbs.

(b) If [tex]w(t)=7.42+1.92t-0.0074t^2+0.000446t^3[/tex]

Rate of change, [tex]w'(t)=1.92-0.0148t+0.001338t^2[/tex]

At t=7 months

[tex]w'(7)=1.92-0.0148(7)+0.001338(7)^2\\w'(7)=1.88$ lbs/month[/tex]

The rate of change for the baby's weight with respect to time at age 7 months is approximately 1.88 lbs/month.

Answer:

The y-intercept is at (0, 250)

It means that there is a flat fee of $250 when hosting a dinner

Step-by-step explanation:

The y-intercept is 250 because in the equation y = mx +b, b is the y-int

It represents a $250 flat fee because it is automatically charged, no matter how many attend the dinner

Answer:

Dear preshoo

Answer to your query is provided below

She read 4 non fiction books during the summer.

Step-by-step explanation:

Bianca read 11 novels.

According to question,

2x Nonfiction books = 11 novels - 3 books

This implies, Non- fiction books = (11-3)/2 = 4books

4 nonfiction books did Bianca read during the summer.

Two or more expressions with an Equal sign is called as Equation.

Given that Bianca read 11 novels.

These 11 novels are 3 more than twice the number of nonfiction books she reads.

we need to find the number of nonfiction books did she read during the summer.

Let x be the nonfiction books.

Twice the number of nonfiction books means 2x and  3 more than it means 2x+3.

2x+3=11

Now subtract 3 from both sides

2x=8

Divide both sides by 2

x=4

Hence, 4 nonfiction books did Bianca read during the summer.

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Answer:

1. it has different colors

Answer:

[tex]\boxed{\sf \ \ \ x^3+8x^2+11x-20 \ \ \ }[/tex]

Step-by-step explanation:

hello,

(x+5)(x+4)(x-1) is one example of polynomial which has roots of -5,-4 and 1

[tex](x+5)(x+4)(x-1) = (x+5)(x^2-x+4x-4)=(x+5)(x^2+3x-4)\\= x^3+3x^2-4x+5x^2+15x-20=x^3+8x^2+11x-20[/tex]

hope this helps

Answer:

No value of k will make AB=BA

Step-by-step explanation:

[tex]A=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right), $ $B=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right) \\\\\\AB=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)=\left(\begin{array}{ccc}3*2+2*-3&3*6+2*k\\-1*2+2*-3&-1*6+2k\end{array}\right)=\left(\begin{array}{ccc}0&18+2k\\-8&-6+2k\end{array}\right)[/tex]

[tex]BA=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)=\left(\begin{array}{ccc}0&16\\-6&-6+2k\end{array}\right)[/tex]

We can see that [tex]AB \neq BA[/tex]. Therefore, there is no value of k that will make it equal. In general, matrix multiplication is not commutative.

Answer:

Step-by-step explanation:

A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.

Given: parallelogram ABCD

          AD≅ BC

          AD ║ BC

Thus;

<ABC + DAB = [tex]180^{o}[/tex] (supplementary angle property)

ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)

<ABC = <ADC (both pairs of opposite angles are congruent)

<DAB = <BCD (both pairs of opposite angles are congruent)

AB ≅ CD (opposite sides are congruent)

AB ║ DC (pair of opposite sides are parallel)

Therefore, the quadrilateral ABCD is a parallelogram.

Answer:

There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.

Step-by-step explanation:

We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.

Let [tex]\mu[/tex] = population mean market value of houses in the neighborhood.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $250,000      {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $250,000      {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}

The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;

                              T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean market value = $259,860

            s = sample standard deviation = $24,922

            n = sample of houses = 35

So, the test statistics  =  [tex]\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                     =  2.34

The value of t-test statistic is 2.34.

Also, P-value of the test statistics is given by;

            P-value = P([tex]t_3_4[/tex] > 2.34) = 0.0137

Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.

Answer:

Step-by-step explanation:

Number of frames =3 frames

If each frames contain 2 photos, the total number of photos in all the 3 frames will be 3*2 = 6photos

Since we have 6 photos in total, the fraction that shows one photo will be ratio of one out of the six photos and this is represented as 1/6

Answer:

All real numbers greater than or equal to 2

Step-by-step explanation:

The range is from bottom to top. Since it is a closed circle this includes 2

The range of the function on the graph is,

''All the numbers greater than or equal to 2.''

The range of a function refers to all the possible values y could be.

The formula to find the range of a function is,

y = f(x).

And, In a relation, it is only a function if every x value corresponds to only one y value.

Here, form the graph;

A closed circle is shown that contains 2.

Hence, The range of the function on the graph is,

''All the numbers greater than or equal to 2.''

So, Option 4 is true.

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Answer:

500g Jelly beans $9.90

Step-by-step explanation:

To know the values.

Let's know how much a gram will cost in each case

300g Jelly beans $5.80

1g = 5.8/300

1 g = 0.01933

500g Jelly beans $9.90

1g = 9.9/500

1g =0.0198

It's obvious that the second one has more value placed on it as it cost more per gram

Answer:

a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.

b. Test statistic z=-1.001

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]

The significance level is 0.01.

The sample has a size n=199.

The sample proportion is p=0.462.

[tex]p=X/n=92/199=0.462[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]

As the P-value (0.16) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.

Answer:

a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

[tex]P(t) = P(0)(1-r)^{t}[/tex]

In which P(0) is the initial amount and r is the decay rate.

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

[tex]P(1) = 0.97P(0)[/tex]

Then

[tex]P(t) = P(0)(1-r)^{t}[/tex]

[tex]0.97P(0) = P(0)(1-r)^{0}[/tex]

[tex]1 - r = 0.97[/tex]

So

[tex]P(t) = P(0)(0.97t)^{t}[/tex]

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

[tex]P(t) = P(0)(0.97t)^{t}[/tex]

[tex]0.5P(0) = P(0)(0.97t)^{t}[/tex]

[tex](0.97)^{t} = 0.5[/tex]

[tex]\log{(0.97)^{t}} = \log{0.5}[/tex]

[tex]t\log{0.97} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.97}}[/tex]

[tex]t = 22.76[/tex]

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

[tex]P(t) = P(0)(0.97t)^{t}[/tex]

[tex]0.85P(0) = P(0)(0.97t)^{t}[/tex]

[tex](0.97)^{t} = 0.85[/tex]

[tex]\log{(0.97)^{t}} = \log{0.85}[/tex]

[tex]t\log{0.97} = \log{0.85}[/tex]

[tex]t = \frac{\log{0.85}}{\log{0.97}}[/tex]

[tex]t = 5.34[/tex]

5.34 years for the sample to decay to 85% of its original amount

The half life of the substance is 22.76 years

Half life is given by:

[tex]N(t)=N_o(\frac{1}{2} )^\frac{t}{t_\frac{1}{2} } \\\\Where\ N(t)\ is \ the \ value\ of\ the\ substance\ after\ t\ years,N_o\ is\ the\\original\ value\ and\ t_\frac{1}{2} \ is\ the\ half\ life[/tex]

Given that t = 1 years, N(t) = 97% of normal amount = 0.97N₀. Hence:

a)

[tex]0.97N_o=N_o(\frac{1}{2} )^\frac{1}{t_\frac{1}{2} } \\\\0.97=(\frac{1}{2} )^\frac{1}{t_\frac{1}{2} }\\\\ln(0.97)=\frac{1}{t_\frac{1}{2} }ln(0.5)\\\\t_\frac{1}{2} =22.76\ years[/tex]

b)

[tex]0.85N_o=N_o(\frac{1}{2} )^\frac{t}{22.76} \\\\0.85=(\frac{1}{2} )^\frac{t}{22.76}\\\\ln(0.85)=\frac{t}{22.76}ln(0.5)\\\\t=5.3\ years[/tex]

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Answer:

a) The two distributions have the same median (6) but the 2nd distribution has a larger IQR (9.5 > 4).

b) The two distributions have a different median with distribution 2 having a bigger median (8 > 3), but they both have the same IQR (3).

c) The 2nd distribution has a slightly bigger median (7 > 6) and a slightly bigger IQR (4.5 > 4) than the 1st distribution.

d) The 2nd distribution consists of variables that are way bigger than those of the 1st distribution, hence, the median and IQR of the 2nd distribution are about ten folds of that of the 1st distribution.

Step-by-step explanation:

For any distribution,

The median is the variable at the middle when all the variables in the dsitribution are arranged in ascending or descending order.

The median is the (n+1)/2 th variabke.

where n = size of the distribution or number of variables. For these questions, the sample size is 5, hence, the median will always be the 3rd variable when the variables are arranged in ascending or descending order.

The IQR, known as the inter quartile range is a measure of dispersion for the distribution. Although, it isn't as effective as other measures of dispersion such as the standard deviation because the IQR unlike the the standard deviation isn't responsive to changes in the variables, especially ones at the end of the distribution.

The IQR is simply given mathematically as the third quartile minus the first quartile.

IQR = (Third quartile) - (First quartile)

Third quartile is the 3(n+1)/4 th variable. For a sample of n=5, the third quartile is the 4.5th variable, that is the average of the 4th and 5th variable.

First quartile is the (n+1)/4 th variable. For a sample of n=5, the first quartile is the 1.5th variable, that is the average of the 1st and 2nd variable.

Taking the questions one at a time

a) (1) 3,5,6,7,9

Median = 3rd variable = 6

Third quartile = (7+9)/2 = 8

First quartile = (3+5)/2 = 4

IQR = 8 - 4 = 4

(2) 3,5,6,7,20

Median = 3rd variable = 6

Third quartile = (7+20)/2 = 13.5

First quartile = (3+5)/2 = 4

IQR = 13.5 - 4 = 9.5

The two distributions have the same median (6) but the 2nd distribution has a larger IQR (9.5 > 4).

b) (1) 1,2,3,4,5

Median = 3rd variable = 3

Third quartile = (4+5)/2 = 4.5

First quartile = (1+2)/2 = 1.5

IQR = 4.5 - 1.5 = 3

(2) 6,7,8,9,10

Median = 3rd variable = 8

Third quartile = (9+10)/2 = 9.5

First quartile = (6+7)/2 = 6.5

IQR = 9.5 - 6.5 = 3

The two distributions have a different median with distribution 2 having a bigger median (8 > 3), but they both have the same IQR (3).

c) (1) 3,5,6,7,9

Median = 3rd variable = 6

Third quartile = (7+9)/2 = 8

First quartile = (3+5)/2 = 4

IQR = 8 - 4 = 4

(2) 3,5,7,8,9

Median = 3rd variable = 7

Third quartile = (8+9)/2 = 8.5

First quartile = (3+5)/2 = 4

IQR = 8.5 - 4 = 4.5

The 2nd distribution has a slightly bigger median (7 > 6) and a slightly bigger IQR (4.5 > 4) than the 1st distribution.

d) (1) 0,10,50,60,100

Median = 3rd variable = 50

Third quartile = (60+100)/2 = 80

First quartile = (0+10)/2 = 5

IQR = 80 - 5 = 75

(2) 0,100,500,600,1000

Median = 3rd variable = 500

Third quartile = (600+1000)/2 =800

First quartile = (0+100)/2 = 50

IQR = 800 - 50 = 750

The 2nd distribution consists of variables that are way bigger than those of the 1st distribution, hence, the median and IQR of the 2nd distribution are about ten folds of that of the 1st distribution.

Hope this Helps!!!

Answer:

[tex] \: \: \: \: \: \: \: \: \: \: \dfrac{x}{5} = 7 \\ \implies \: x = 7 \times 5 \\ \implies \: x = 35[/tex]

So,b. multiplication

Answer:

A. division

Step-by-step explanation:

[tex]x/5=7[/tex]

[tex]x[/tex] is being divided by an integer.

[tex]x=35[/tex]

[tex]35/5=7[/tex]

35 divided by 5 is equal to 7.