At the kennel, the ratio of cats to dogs is 4:5. There are 27 animals in all. How many cats are in the kennel?

Answer:

B. Average of the data set

Step-by-step explanation:

The mean is defined as the average of a data set and it's formula is

Mean = [tex]\frac{sum of observations}{number of observations}[/tex]

Answer:

6.68% probability that the mean weight is below 68.5g.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

Probability that the mean weight is below 68.5g:

This is 1 subtracted by the pvalue of Z when X = 68.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{68.5 - 70}{1}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that the mean weight is below 68.5g.

Answer:

P(x ∠ 68.5) = 0.07

Step-by-step explanation:

Got it right on khan.

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

substitute

[tex]d = \sqrt{((-3) - (-6))^2 + ((9)-(8))^2}[/tex]

[tex]\sqrt{10}[/tex]

Answer:

B.

Step-by-step explanation:

A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.

Answer: (b) 15.07 to 19.93 miles

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 3.8

n = number of samples = 20

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 20 - 1 = 19

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.02/2 = 0.005

the area to the right of z0.005 is 0.025 and the area to the left of z0.025 is 1 - 0.005 = 0.995

Looking at the t distribution table,

z = 2.861

Margin of error = 2.861 × 3.8/√20

= 2.43

the lower limit of this confidence interval is

17.5 - 2.43 = 15.07 miles

the upper limit of this confidence interval is

17.5 + 2.43 = 19.93 miles

Answer:

325 square inches

Step-by-step explanation:

Consider the attachment below for further reference. Ideally we would split this figure into parts, and solve as demonstrated by the attachment. I have labeled each rectangle as rectangle 1, rectangle 2, rectangle 3 etc. ;

[tex]Rectangle 1 Area = 17 in * 5 in = 85 square in\\Rectangle 2 Area = ( 17 in - 5 in ) * 14 in = 168 square in,\\Rectangle 3 Area = ( 12 in - 3 in ) * 8 in = 72 square in\\\\Total Area = 85 + 168 + 72 = 325 square inches[/tex]

Hope that helps!

Answer: The answer is 325 inches.

Step-by-step explanation: You can divide the rectangle into multiple parts and find the areas of those parts and add all the areas together at the end

Answer:

a) 5/9

b) 1/3

Step-by-step explanation:

a) P(Die A or Die B) = P(red and red with Die A) + P(red and red with Die B)

                               = 4/6 × 4/6 +  2/6×2/6

                               = 5/9

b)  P(Die A or Die B) = P(red and red and red with Die A) + P(red and red and red with die B)

                           = 4/6×4/6×4/6 + 2/6×2/6×2/6

                          = 1/3

Answer:

The answer is 8300.

Step-by-step explanation:

1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.

2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.

Answer:

ITS C

Step-by-step explanation:

The other answer is wrong, I just tried it.

Answer:

It's C on EDG

Step-by-step explanation:

easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

Answer: The new price of  the car is $41856

Step-by-step explanation:

So we know the the original price as 43,600 which is 100% and is being dropped by 4%  so you would have to subtract 4% from a 100% and multiply it by the original price.

100% - 4% = 96%

Now 96% of the original price is the new price.

96% * 43,600= ?

0.96 * 43,600 = 41856

Answer:

a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]

And from the empirical rule we know that this probability is 0.997 or 99.7%

b)[tex] P(195.2 <X<322.2)[/tex]

Using the z score we have:

[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]

[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]

And within one deviation from the mean we have 68% of the values

Step-by-step explanation:

For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:

[tex] \mu = 258.7, \sigma =63.5[/tex]

Part a

We can use the z score formula given by:

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

And we want this probability:

[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]

And from the empirical rule we know that this probability is 0.997 or 99.7%

Part b

For this case we want this probability:

[tex] P(195.2 <X<322.2)[/tex]

Using the z score we have:

[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]

[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]

And within one deviation from the mean we have 68% of the values

Answer:

You can't find the next solution without more information.

Step-by-step explanation:

Answer:

746 mi^2

Step-by-step explanation:

The top rectangle has an area of

A = 22*23 =506

The bottom rectangle has an area of

A =10 *24 = 240

Add the areas together

506+ 240 =746

Answer:

746

Step-by-step explanation:

22*23= 506

24*10= 240

506+240= 746

plz mark brainliest

Answer:

[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]

So the answer for this case would be n=247 rounded up to the nearest integer

Step-by-step explanation:

We know that the standard deviation is :

[tex]\sigma = 80[/tex] represent the deviation

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution and the critical value would be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]

So the answer for this case would be n=247 rounded up to the nearest integer

Answer:

The standard unemployment rate is of 0.0794 = 7.94%.

Step-by-step explanation:

The standard unemployment rate, as a proportion, is the number of unemployed people divided by the size of the labor force.

In this question:

Labor force: 189 million

Number of unemployed people: 15 million

What is the standard unemployment rate?

15/189 = 0.0794

The standard unemployment rate is of 0.0794 = 7.94%.

            ∠FGK and ∠FGH               Im pretty sure its right

A ray is a half-infinite line. The pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.

A half-infinite line (also known as a half-line) with one of the two points and is commonly used to represent a ray. It is assumed to be infinite.

A straight line has an angle of measurement of 180°. And a 90° angle is made when two lines are perpendicular to each other.

As we can see the line EGH is a straight line, and FG is another line that is perpendicular to line EH, therefore, it will form two angles measuring 90°. These angles will be ∠FGE and ∠FGH.

Hence, the pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.

Learn more about Ray:

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Answer:

c

Step-by-step explanation:

when the absolute value of slope gets smaller, the graph of line gets less steeper.

Answer:

3a) 30% more than original price

b) 70% of the original price

c) 17times the original price

d) 70% less than original price

e) t + 0.85t

f) t - 0.15t

g) t - 0.85t

h) t + 0.15t

4. The expression that can be used to find the amount of money in his bank = m + 0.25m

Question:

3. Match each statement with an expression that could be used to find the price.

'The expressions for a to d were not stated in the question'.

a) p+ 0.3p

b) 0.7p

c) 17p

d) p-07p

'From e to h, we were not told what to determine'.

Write the expression in terms of time

e. 85% more than the original time

f. 15% less time than the original

g. 85% time decrease

h. 15% time increase

4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original​.

Step-by-step explanation:

let original price = p

a) p+ 0.3p = p + 30% of p

30% more than original price

b) 0.7p = 70% of p

= 70% of the original price

c) 17p = 17 × p

= 17times of the original price

d) p-0.7p = p - 70% of p

= 70% less than original price

Let original time = t

e) 85% more than the original time = t + 85%of t

= t + 0.85t

f) 15% less time than the original time = t - 15% of t

= t - 0.15t

g) 85% time decrease = t - 85% of t

= t - 0.85t

h) 15% time increase = t + 15% of t

= t + 0.15t

4. Since "m" represent the original amount in Hus piggy bank

An increase of 25% = original amount + 25% of original amount

= m + 25% of m

'Of' means multiplication

= m + 0.25 ×m

= m + 0.25m

= 1.25m

The expression that can be used to find the amount of money in his bank = m + 0.25m

Answer:

The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].

Step-by-step explanation:

The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.

For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.

These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155. How many standard deviations from the mean is the value 155?

From the question, we know that:

Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject   earned a score that equals the population mean. Then, using [1]:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{155 - 155}{50}[/tex]

[tex] \\ z = \frac{0}{50}[/tex]

[tex] \\ z = 0[/tex]

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:  

[tex] \\ x = \mu[/tex]

Therefore

[tex] \\ z = 0[/tex]

So, the value 155 is zero standard deviations from the [population] mean.

Answer:

the triangles are not similar.

Answer:

the answer is 6!!!!!!

Step-by-step explanation:

The missing value in the table is 5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

An intravenous fluid is infused at the rate shown in the table

Minutes         Milliliters

3                            4

?                             12

2.                            3

?                             6

3                             9

9                             24

Slope=24-9/9-3

=15/3

=5

Now 5=12-4/x-3

5=8/x-3

5x-15=8

5x=23

x=23/5

x=4.6

x=5

The missing number is 5.

Hence, the missing value in the table is 5

To learn more on slope of line click:

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Answer:

The speed of the river is 2mph.

Step-by-step explanation:

I guess that we want to find the speed of the river.

First, remember the relation: speed*time = distance

If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:

Sd = 4mph + Sr

and at this speed, in a time T, she can move 21 miles, so we have:

Sd*T = (4mph + Sr)*T = 21 mi

When moving upstream, the speed will be:

Su = (4mph - Sr)

and in the same time T as before, she moves 7 miles, so we have the equation:

Su*T = (4mph - Sr)*T = 7 mi

Then we have two equations:

(4mph + Sr)*T = 21 mi

(4mph - Sr)*T = 7 mi

Now we can take the quotient of those two equations and get:

((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7

The time T vanishes, and we can solve it for Sr.

(4mph + Sr)/(4mph - Sr) = 3

4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr

4*Sr = 12mph - 4mph = 8mph

Sr = 8mph/4 = 2mph.

Answer:

1<X<=6

Step-by-step explanation:

seven less than six times her number is between negative one and twenty-nine (inclusive).

The above statement can be expressed mathematically thus;

Let the number be x

6x-7= (-1 ,29]

Hence 6x-7 = -1=>6x=6=>x=1 or

6x-7= 29=>6x=36=>x=6

Hence 1<X<=6

Answer:

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Step-by-step explanation:

We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.

The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Answer:

The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.

1. When x=-1, then

f(-1) = 2 * (-1)^3 - 3 * (-1)^2 + 7 = -2 - 3 + 7 = 2.

2. When x=1, then

f(1) = 2 * 1^3 - 3 * 1^2 + 7 = 2 - 3 + 7 = 6.

3. When x=2, then

f(-1) = 2 * 2^3 - 3 * 2^2 + 7 = 16 - 12 + 7 = 11.

Step-by-step explanation:

Answer:

f(−1) =✔ 2

f(1) = ✔ 6

f(2) =✔ 11

Step-by-step explanation:

Answer:

28 and 32

Step-by-step explanation:

they have the most

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: standardized history test score in third grade.

X₁: final percentage in history class.

X₂: number of absences per student.

Determine the following multiple regression values.

I've estimated the multiple regression equation using statistics software:

^Y= a + b₁X₁ + b₂X₂

a= 118.68

b₁= 3.61

b₂= -3.61

^Y= 118.68 + 3.61X₁ - 3.61X₂

ANOVA Regression model:

Sum of Square:

SS regression: 25653.86

SS Total: 36819.23

F-ratio: 11.49

p-value: 0.0026

Se²= MMError= 1116.54

Hypothesis for the number of absences:

H₀: β₂=0

H₁: β₂≠0

Assuming α:0.05

p-value: 0.4645

The p-value is greater than the significance level, the decision is to not reject the null hypothesis. Then at 5% significance level, there is no evidence to reject the null hypothesis. You can conclude that there is no modification of the test score every time the number of absences increases one unit.

I hope this helps!

Answer:

Step-by-step explanation:

The given equations are

x + y = 6- - - - - - - - -1

y + z = 6- - - - - - - -2

x + z = 6- - - - - - - - - 3

From equation 2, y = 6 - z

Substituting y = 6 - z into equation 1, it becomes

x + 6 - z = 6

x - z = 6 - 6

x - z = 0

x = z

Substituting x = z into equation 3, it becomes

z + z = 6

2z = 6

z = 6/2

z = 3

x = 3

Substituting x = 3 into equation 1, it becomes

3 + y = 6

y = 6 - 3

y = 3

ax + by + cz = 0

3a + 3b + 3c = 0

3(a + b + c) = 0

Therefore, it is impossible

Complete Question

From the mid-1960's to the early 1990's, there was a slow but steady decline in SAT scores. For example, take the Verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the SD stayed close to 110. The drop in average has a large effect on the tails of the distribution.

Estimate the percentage of students scoring over 700 on 1967.

A 0.7%

B  7%

C 7.67%

D 7.6%

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

   The average  SAT score in 1967 is  [tex]\= x_1 =543[/tex]

     The  standard deviation of score in 1967 is  [tex]\sigma_ 1= 110[/tex]

     The average  SAT score in 1994 is  [tex]\= x_2 = 499[/tex]

      The  standard deviation of score in 1967 is  [tex]\sigma_ 2 = 110[/tex]

The percentage of students scoring over 700 on 1967 is mathematically represented as

   [tex]P(X > 700)[/tex]

Where X is the random variable representing score of student above 700

Now  normalizing the above probability we have

     [tex]P(X > 700) = P(Z > \frac{700 - \= x_1 }{\sigma } )[/tex]

substituting values

      [tex]= P(Z > \frac{700 - \= 543}{110 } )[/tex]

      [tex]= P(Z > 1.83 )[/tex]

Form the normalized z table  

      =  0.076

     =  7.6 %