"Her eyes shone as bright as the sun" is an example of
Is it a simile of idiom

listen yeah

plot the points on the graph and join up dots

then draw a line x = 4 so 4 on x axis draw a vertical line as its line of symmetry

then reflect the shape

for the x co ordinates, say that they are different because the x values are not the same

for the y co ordinates, say thay they are the same because the y values did not change

plot points on 2nd graph and join up dots

then draw a line y = 2 so 2 on y axis draw a horizontal line as its line of symmetry

then reflect shape

for the x co ordinates, say that they are the same because the x values did not change

for the y co ordinates, say that they are different because the y values are not the same

Answer:

Paul is the youngest at 17 years old. Fiona is 20 years old, Sara is 23 years old

Step-by-step explanation:

Assign variables to the ages.

S = sara's age

F = Fiona's age

P = Paul's age.

S + F + P = 60

S = 3 + F

P = F - 3

(3 + F) + F + (F - 3) = 60

3 + 3F - 3 = 60

3F = 60

F = 20

S = 23

P = 17

Answer:

[tex]z=\frac{514-600}{\frac{112}{\sqrt{67}}}=-6.285[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-6.285)=1.64x10^{-10}[/tex]  

Since the p value is very low than the significance level given we have enough evidence to conclude that the true mean for the scores on a standardized memory is significantly lower than 600 and then we can conclude that memory performance is reduced by old age

Step-by-step explanation:

Information given

[tex]\bar X=514[/tex] represent the sample mean for the scores on a standardized memory

[tex]\sigma=112[/tex] represent the population standard deviation

[tex]n=67[/tex] sample size  

[tex]\mu_o =600[/tex] represent the value that we want to verify

[tex]\alpha=0.1[/tex] represent the significance level  

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to check if the true mean for this case is less than 600, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 600[/tex]  

Alternative hypothesis:[tex]\mu < 600[/tex]  

Since we know the population deviation the statistic for this case is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{514-600}{\frac{112}{\sqrt{67}}}=-6.285[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-6.285)=1.64x10^{-10}[/tex]  

Since the p value is very low than the significance level given we have enough evidence to conclude that the true mean for the scores on a standardized memory is significantly lower than 600 and then we can conclude that memory performance is reduced by old age

The answer is D.) (13,0)

I remember seeing this question somewhere before... Along with the graph.

Additionally, make sure to add the graph to the question next time!

The coordinates of focus are ( 13, 0)

The hyperbola can be defined as the difference of distances between a set of points, which are present in a plane to two fixed points is a positive constant.

A hyperbola is a set of points whose difference of distances from two foci is a constant value. This difference is taken from the distance from the farther focus and then the distance from the nearer focus. For a point P(x, y) on the hyperbola and for two foci F, F', the locus of the hyperbola is PF - PF' = 2a.

We know,

Foci for hyperbola is : (c,0) and (−c,0)

As, from the attached graph below the focus is:

Focus : ( 13, 0)

Hence, the Focus is: ( 13, 0).

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Answer:

[tex]z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8[/tex]  

[tex]p_v =2*P(z<-0.760)=0.447[/tex]  

Step-by-step explanation:

Information given

n=564 represent the sample selected

X=51 represent the number of people who rated the overall services as poor

[tex]\hat p=\frac{51}{564}=0.0904[/tex] estimated proportion of people who rated the overall services as poor  

[tex]p_o=0.1[/tex] is the value to compare

z would represent the statistic

Hypothsis to analyze

We want to analyze if the proportion of customers who would rate the overall car rental services as poor is 0.1, so then the system of hypothesis are:  

Null hypothesis:[tex]p=0.1[/tex]  

Alternative hypothesis:[tex]p \neq 0.1[/tex]  

The statistic for a one z test for a proportion is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8[/tex]  

And the p value since we have a bilateral test is given b:

[tex]p_v =2*P(z<-0.760)=0.447[/tex]  

The question is about testing a null hypothesis in a customer satisfaction survey for a software company. The null hypothesis is that 10% of customers would rate the services as poor. The calculated test statistic was approximately -1.3.

The question involves testing a null hypothesis regarding the proportion of customers who would rate the software company's services as poor. We are given that a total of 564 customers took part in the survey, out of which 51 rated the services as poor. Here, the null hypothesis is that 10% (or 0.1) of customers would rate the services as poor.

To test the null hypothesis, we compare the sample proportion to the claimed proportion (0.1). The sample proportion in this case is 51/564 = 0.0904. We can calculate the test statistic using the formula for sample proportion, which is (p' - p) / sqrt [ p * (1 - p) / n ], where p is the claimed proportion, p' is the sample proportion, and n is the sample size. In this case, the test statistic would be approximately (0.0904 - 0.1) / sqrt [0.1 * (1 - 0.1) / 564] = -1.3 (rounded to the first decimal).

The p-value corresponds to the test statistic under the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis. But here, we didn't calculate the p-value as it wasn't part of the question, so we won't make a decision on the null hypothesis.

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We have been given that a new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by [tex]3^x[/tex], where x is the time, in seconds. We are asked to find the time when the height of the rocket id 8 miles.

To find the time, we will equate height function with 8 and solve for x as:

[tex]3^x=8[/tex]

To solve for x, we will take natural log on both sides as:

[tex]\ln(3^x)=\ln (8)[/tex]

We can rewrite 8 as [tex]2^3[/tex].

[tex]\ln(3^x)=\ln (2^3)[/tex]

Using natural log property [tex]\ln(a^b)=b\cdot \ln(a)[/tex], we will get:

[tex]x\cdot \ln(3)=3\cdot\ln (2)[/tex]

[tex]\frac{x\cdot \ln(3)}{ \ln(3)}=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]

[tex]x=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]

Therefore, exact solution will be [tex]\frac{3\cdot\ln (2)}{ \ln(3)}[/tex].

[tex]x=\frac{2.0794415416798359}{1.0986122886681097}[/tex]

[tex]x=1.892789260714[/tex]

Upon rounding to nearest thousandth, we will get:

[tex]x\approx 1.89[/tex]

Therefore, the height of the rocket will be 8 miles after approximately 1.89 seconds.

Answer:

The correct answer is A

Step-by-step explanation:

1,260 divided by 180 = 7

180 times 6 = 1,080

180 times 7 = 1,260

If the car traveled 1260 miles, then 42 gallons of gas would be used.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the amount of gas consumed by a car varies directly with the miles driven.

Using the formula for direct proportionality -

y₁/x₁ = y₂/x₂

180/6 = 1260/x₂

x₂ = (1260 x 6)/180

x₂ = (126 x 6)/18

x₂ = (21 x 2)

x₂ = 42

Therefore, If the car traveled 1260 miles, then 42 gallons of gas would be used.

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Answer:

552.78

Step-by-step explanation:

45 x 6 =270

2πr = r x 2 x 3.142 = 45 x 2 x 3.142 = 282.78

270 + 282.78

The total length of the steel when both the circular section is added would be = 552.6cm.

The total length of the steel can be calculated following the steps below:

The total length of the 6 stems with 45cm = 45×6 = 270cm

The length of circular section = 2πr

where r = 45cm

C = 2× 3.14×45

= 282.6

The total length = 270+ 282.6

= 552.6cm

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Answer:

327

Step-by-step explanation:

7 ones = 7*1 = 7

2 tens = 2*10 = 20

3 hundreds = 3 * 100 = 300

300 +20 +7 = 327

Answer:

20

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

12^2+16^2 = c^2

144+256 = c^2

400 = c^2

Take the square root of each side

sqrt(400) = sqrt(c^2)

20 = c

Answer:

(C)18 Units

Step-by-step explanation:

Volume of a Triangular Prism =Base Area X Height

The base is a right triangle of base 8 Units and Height 15 Units.

Area of the Triangle =0.5 x 8 x 15 =60 Square Units

Base Area, B=60 Square Units

Since Volume of the Triangular Prism=1080

1080=60h

Divide both sides by 60

Height of the Prism=18 Units

Answer:

The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.

Step-by-step explanation:

The random variable X is defined as the time a new thunderstorm begins to produce rain.

The random variable X is uniformly distributed throughout the day, i.e. between the 24 hours a day or 1440 minutes.

[tex]X\sim Uniform\ [0, 1440][/tex]

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

It is provided that it will rain at some point both of the next two days.

Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM as follows:

9:10 AM = (9 × 60) + 10 = 550 minutes.

3:30 PM = 15:30 = (15 × 60) + 30 = 930 minutes.

Compute the value of P (550 < X < 930) as follows:

[tex]P(550<X<930)=\int\limits^{930}_{550}{\frac{1}{1440-0}}\, dx\\\\=\frac{1}{1440}\times \int\limits^{930}_{550}{1}\, dx\\\\=\frac{1}{1440}\times [x]^{930}_{550}\\\\=\frac{930-550}{1440}\\\\=0.2639[/tex]

The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM is 0.2639.

Then the complement of this event is:

The probability that the first drop of rain will not be felt between 9:10 AM and 3:30 PM is:

P (Not between 9:10 AM and 3:30 PM) = 1 - 0.2639 = 0.7361

Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days as follows:

P (At least 1) = 1 - P (Less than 1)

                    = 1 - P (None)

                    = 1 - P (Not between 9:10 AM and 3:30 PM)

                    = 1 - 0.7361

                    = 0.2639

Thus, the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.

Answer: 42

Step-by-step explanation:

convert 5 1/4 to an improper fraction=21/4

then multiply 21/4 • 8 = 42!

hope this helps (:

The volume of the rectangular prism is, 42 units³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

For a rectangular prism,

Base area = 5 1/4 units

Height = 8 units

We know that;

The volume of the rectangular prism = Base area x Height

Substitute given values, we get;

The volume of the rectangular prism = Base area x Height

The volume of the rectangular prism = 5 1/4 x 8

The volume of the rectangular prism = 21/4 x 8

The volume of the rectangular prism = 42 units³

Thus, The volume of the rectangular prism is, 42 units³

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Answer:

x=46 gives us the minimum value

Step-by-step explanation:

Let us have the height of the box to be y. Since the box has a square base, let us call the side of the base as x. So, the volume of the box is given by

[tex]x^2\cdot y = 48668[/tex]. From here, we know that [tex]y=\frac{48668}{x^2}[/tex]

Now, we will find the area of the box. Since the box has an open top, then we only have the 4 sides of the box and the base. The base is a square of side x, so its area is [tex]x^2[/tex]. Recall that each side is a rectangle of base x and height y. So, the are of one side is [tex]x\cdot y[/tex]. Then, the area of the box is given by the function

[tex]A(x,y) = x^2+4xy[/tex]. Since we can relate y to x through the volume, this can be a function of one variable. Namely

[tex]A(x) = x^2+4x\cdot \frac{48668}{x^2}= x^2+4\cdot \frac{48668}{x} = x^2+48668x^{-1}[/tex]

If we want to find the mininum value, we should derive the function A and find the value of x for which A'(x) is zero. REcall that the derivative of a function of the form [tex]x^n[/tex] is [tex]nx^{n-1}[/tex]. Then, applying the properties of derivatives, we have

[tex] A'(x) = 2x-4\cdot \frac{48668}{x^2} = \frac{2x^3-4\cdot 48668}{x^2}[/tex]

So, we want to solve the following equation

[tex]2x^3-4\cdot 48668 =0[/tex]

which implies [tex]x^3 = 97336[/tex]. Using a calculator we get the value [tex] x= 46[/tex]

REcall that to check if the point is a minimum, we use the second derivative criteri. It states that the point x is a mininimum if f'(x) =0 and f''(x)>0

Note that [tex]A''(x) = 2+8\cdot\cdot 48668}{x^3}[/tex], note that A''(46) = 6>0, so x=46 is the minimum value of the area.

To find the formula for the surface area of the box in terms of only the length of one side of the square base, express the height of the box in terms of x. The formula for the surface area is S = 194672 / x + x².

To find the formula for the surface area of the box in terms of only the length of one side of the square base, we need to express the height of the box in terms of x. The volume of the box is given as 48668 cm³, which is equal to the base area (x²) multiplied by the height (h). So, we have the equation x² * h = 48668. Solving for h, we get h = 48668 / x².

The surface area of the box consists of the area of the four sides of the box (4 * x * h) and the area of the square base (x²). We can substitute the value of h in terms of x into this expression to get the simplified formula for the surface area: S = 4 * x * (48668 / x²) + x². Simplifying further, we get S = 194672 / x + x².

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Answer:

Her average speed is 48 miles per hour.

Step-by-step explanation:

We solve this question using a system of equations.

The speed equation is:

[tex]s = \frac{d}{t}[/tex]

In which s is the speed, d is the distance, and t is the time.

Gabriella drives her car 320 miles and averages a certain speed.

So [tex]d = 320[/tex]

Then

[tex]s = \frac{320}{t}[/tex]

If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time.

So, which s - 6, d = 280.

[tex]s - 6 = \frac{280}{t}[/tex]

From the first equation:

[tex]s = \frac{320}{t}[/tex]

[tex]st = 320[/tex]

[tex]t = \frac{320}{s}[/tex]

Replacing:

[tex]s - 6 = \frac{280}{t}[/tex]

[tex]s - 6 = \frac{280}{\frac{320}{s}}[/tex]

[tex]320(s - 6) = 280s[/tex]

[tex]320s - 1920 = 280s[/tex]

[tex]40s = 1920[/tex]

[tex]s = \frac{1920}{40}[/tex]

[tex]s = 48[/tex]

Her average speed is 48 miles per hour.

Answer:

282.7431 cm^2 (Lateral Surface Area)

Step-by-step explanation:

If you didn't need Lateral Surface Area let me know and I'll see what I can do :3

The correct answer is that the probability of the random variable having an outcome of 3 is 0.

To solve this problem, we need to understand that the random variable assigns the number of blue marbles drawn to each outcome of the experiment. Since the experiment consists of two independent draws with replacement, there are four possible outcomes:

1. Draw a blue marble, then draw another blue marble.

2. Draw a blue marble, then draw a red marble.

3. Draw a red marble, then draw a blue marble.

4. Draw a red marble, then draw another red marble.

The probability of drawing a blue marble in a single draw is given as 3/8. Therefore, the probability of drawing a red marble is the complement of this, which is 1 - 3/8 = 5/8.

Now, let's calculate the probability of each of the four outcomes:

1. The probability of drawing two blue marbles (BB) is (3/8) * (3/8), because the draws are independent.

2. The probability of drawing a blue marble followed by a red marble (BR) is (3/8) * (5/8).

3. The probability of drawing a red marble followed by a blue marble (RB) is (5/8) * (3/8).

4. The probability of drawing two red marbles (RR) is (5/8) * (5/8).

Since the random variable assigns the number of blue marbles to each outcome, the only way to have an outcome of 3 is to draw a blue marble, then draw another blue marble. This is the first outcome listed above.

The probability of drawing two blue marbles (BB) is (3/8) * (3/8) = 9/64.

However, the question asks for the probability of the random variable having an outcome of 3. Since the maximum number of blue marbles that can be drawn in two draws is 2, it is impossible to have an outcome of 3. Therefore, the probability of the random variable having an outcome of 3 is 0.

In conclusion, the probability that the random variable has an outcome of 3 is 0, because it is not possible to draw more than 2 blue marbles in two independent draws with replacement from a bag where the probability of drawing a blue marble is 3/8.

Answer:

Red-5-0.1

Blue-0.26

White-10

Green-22

Step-by-step explanation:

In the experiment, Alexis drew colored balls and you need to organize the results in a frequency table. The numbers given represent frequency counts for each color. Keep in mind that the total draws were 50, so no frequency count should exceed this number.

The question is about Alexis' experiment involving drawing colored balls from a box. The results of the 50 trials are recorded in a frequency table. As the student, you are expected to correctly assign certain numbers to their respective places in this table. These numbers represent the total counts per color across the 50 trials.

To accomplish this, you must first understand what a frequency table is. A frequency table is a method of organizing raw data in a compact form by displaying a series of data values in ascending order, along with their corresponding frequencies.

In this scenario, the frequencies are the number of times Alexis drew a ball of a specific color. For example, if she drew a red ball 15 times, we would put 'Red' in the color column and '15' in the frequency column.

Please note that not all the provided numbers will be used, and there should be no number in the table higher than 50 since that was the maximum number of trials Alexis performed.

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Answer:

16.16 or 16 inch

Step-by-step explanation:

you can use the pythagoras theorem,

h = 19

so, width = [tex]\sqrt{19^2 - 10^2}[/tex]

Answer:

16.16 or 16 inch

Answer:

explanation

Step-by-step explanation:

The Range (Statistics) The Range is the difference between the lowest and highest values. Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. So the range is 9 − 3 = 6.

Answer:

The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.

Answer:

(a) H₀: μ = 5 vs. Hₐ: μ ≠ 5.

(b) The test statistic value is -3.67.

(c) The p-value of the test is 0.0025.

(d) The mean amount of time spent in the shower by an adult is different from 5 minutes.

Step-by-step explanation:

In this case we need to test whether the mean amount of time that college students spend in the shower is significantly different from 5 minutes.

The information provided is:

[tex]n=15\\\bar x=4.29\\s=0.75\\\alpha =0.01[/tex]

(a)

The hypothesis for the test can be defined as follows:

H₀: The mean amount of time spent in the shower by an adult is 5 minutes, i.e. μ = 5.

Hₐ: The mean amount of time spent in the shower by an adult is different from 5 minutes, i.e. μ ≠ 5.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}\\\\=\frac{4.29-5}{0.75/\sqrt{15}}\\\\=-3.67[/tex]

Thus, the test statistic value is -3.67.

(c)

Compute the p-value of the test as follows:

[tex]p-value=2\times P(t_{\alpha/2, (n-1)}<-3.67)\\ =2\times P(t_{0.005, 14}<-3.67)\\=0.0025[/tex]

*Use a t-table.

Thus, the p-value of the test is 0.0025.

(d)

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.0025 < α = 0.01

The null hypothesis will be rejected at 1% level of significance.

Thus, concluding that the mean amount of time spent in the shower by an adult is different from 5 minutes.

Answer:

-16, -25, -34, -43, and -52

Step-by-step explanation:

a, = - 9n - 7.

Sequence given by

a_n, = - 9n - 7.

a_1 = -9*1 - 7 = -16

a_2 = -9*2 - 7 = -18 - 7 = -25

a_3 = -9*3 - 7 = -27 - 7 = -34

a_4 = -9*4 - 7  = -36 - 7 = -43

a_5 = -9*5 - 7 = -45 - 7 = -52

Answer:

A

Step-by-step explanation:

the solid figure that has the shape like a cereal box is a rectangular prism

Answer:

  no

Step-by-step explanation:

Look at the first numbers of each ordered pair:

  4, 8, 4, 20, 12

If any are repeated, the relation is NOT a function. Here, 4 is repeated.

The relation is not a function.

Answer:

8223 cubic meter

Step-by-step explanation:

Louvre Pyramid

Vertical Height =21.6 meters

Side Length of Square Base =35 m

Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]

Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*35^2 X 21.6[/tex]

=8820 cubic meter.

Inverted Pyramid

Vertical Height =7 meters

Side Length of Square Base =16 m

Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]

Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*16^2 X 7[/tex]

=597.33 cubic meter.

Difference in Volume

Difference=Volume of Louvre Pyramid-Volume of Inverted Pyramid

=8820-597.33

=8222.67

=8223 cubic meter (to the nearest cubic meter)

The domain and range of each function y = 3.52 is All real numbers and {3.52}.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are given that;

The function y=3.52

Now,

For the function y = 3.52, the output (y-value) is always the same, regardless of the input (x-value). Therefore, the domain of this function is all real numbers, and the range of this function is the single value 3.52.

Therefore, the domain and range will be All real numbers and {3.52}

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Answer:

Option D is the correct answer - Estimation is best defined as   a process of inferring the values of unknown samples statistics from those of known population parameters

Step-by-step explanation:

Estimation involves the usage of the value of a statistic derived from a sample to estimate the value of a corresponding population parameter.

The sample provides information that can be extended, through several formal or informal processes, to determine a range most suitable to describe the missing information.

An estimate that turns out to be incorrect would either be termed as over-estimation or under-estimation. If the estimate exceeds the actual result, it is termed as an over-estimation, and as an under-estimation, if the estimate came short of the actual result.

Thus, option D is correct.

The best definition of estimation will be E. process of inferring the values of unknown population parameters from those of known sample statistics.

In conclusion, the best option is E.

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