The sum of Jason’s age and his brother’s age is 55. Jason is 7 years younger than his brother. How old is Jason?

Answer:

d) The t-distribution with 5 degrees of freedom must be used

Step-by-step explanation:

For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.

The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.

Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger),  we can assume that the curve of t-student is the same as for normal distribution

Answer:

AC = DF

Step-by-step explanation:

The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.

Answer:

9

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

Hey there!

Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.

Hope this helps :)

Answer:

  10%

Step-by-step explanation:

Using the given formula with the given data, we have ...

  efficiency = output work / input work

  = (10 J)/(100 J) = 0.10 = 10%

Answer:

A) 10%

Step-by-step explanation:

10/100=10

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

Answer:

B. (1,7)

Step-by-step explanation:

We can substitute the x and y values of each coordinate into the inequality and test if they work.

Let's start with A, 5 being y and 0 being x .

[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]

5 IS NOT greater than 5, they are the exact same, so A is out.

Let's try B, 1 being x and 7 being y.

[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]

7 IS greater than 6, so B. (1,7) does work for this inequality!

Let's do C for fun, when 7 is x and 1 is y.

[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]

1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.

Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].

Hope this helped!

Answer:

Step-by-step explanation:

Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same

Let's get the slope of both equation. For the first equation;

y=(3a+2)x-2

We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2

Similarly for the second line;

2y=(a-4)x+2

Re-writing in the standard format we will have;

y = (a-4)x/2+2/2

y = (a-4)x/2 + 1

The slope of the second line is (a-4)/2

On equating the slope of both lines to get the value of 'a' we will have;

3a+2 = (a-4)/2

Cross multiplying

2(3a+2) = a-4

6a+4 = a-4

Collecting like terms;

6a-a = -4-4

5a = -8

a = -8/5

Hence the value of a is -8/5

Answer:

[tex]\boxed{ \sf 41.81}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions.

[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(?)=\frac{2}{3}[/tex]

[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]

[tex]\sf ?= 41.81031489...[/tex]

Answer:

[tex]\boxed{41.81}[/tex]

Step-by-step explanation:

∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.

The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).

However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.

Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.

Answer:

Step-by-step explanation:

Confidence interval for the population mean is expressed by the formula;

CI = xbar ± Z(S/√n) where;

xbar is the sample mean = 12.5

Z is the z score at 99% confidence = 2.576

S is the standard deviation = √variance

S = √2.4 = 1.5492

n is the sample size = 25

Substituting the given values into the formula given above,

CI = 12.5 ± 2.576(1.5492/√25)

CI = 12.5 ± 2.576(0.30984)

CI = 12.5 ± 0.7981

CI = (12.5-0.7981, 12.5+0.7981)

CI = (11.2019, 12.7981)

Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)

A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".

According to the question,

Sample mean, [tex]\bar x[/tex] = 12.5

Z score at 99%, Z = 2.576

Standard deviation, S = √Variance

                                    = √2.4

                                    = 1.5492

Sample size, n = 25

We know the formula,

Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])

By substituting the given values, we get

                                        = 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])

                                        = 12.5 [tex]\pm[/tex] 2.576 (0.30984)

                                        = 12.5 [tex]\pm[/tex] 0.7981

Now,

                                   Cl = (12.5 - 0.7981, 12.5 + 0.7981)

                                        = (11.2019, 12.7981) or,

                                        = (11.2, 12.8)

Thus the above answer is appropriate.        

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Answer:

a = 8.1

Step-by-step explanation:

Firstly, since we have a triangle, automatically, we have 3 interior angles

Mathematically the sum of these angles = 180

A + B + C = 180

27 + 25 + C = 180

52 + C = 180

C = 180-52

C = 128

We use the sine rule to find a

The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle

Thus, mathematically according to the sine rule;

c/Sin C = a/Sin A

14/sin 128 = a/sin 27

a = 14sin27/sin 128 = 8.0657

which to the nearest tenth is 8.1

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

1/5 are towboats

Step-by-step explanation:

In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together

30k + 10k + 10k= 50k

In total there are 50,000 flag vessels

Of those 50,000, 10,000 of them are tow boats

10,000/50,000 can be simplified to 1/5

1/5 are towboats

Answer:

1/5

Step-by-step explanation:

Well to find the fraction we first need to know the total amount of Flag Vessels.

30,000 + 10,000 + 10,000 = 50,000

If there are 10,000 towboats we can make the following fraction.

10,000/50,000

Simplified

1/5

Thus,

the answer is 1/5.

Hope this helps :)

Answer:

see details below

Step-by-step explanation:

The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.

a. Determine the amount to be financed.​​​​​​​15a. ___$23450____________

29450 - 6000 = 23450

b. Determine the installment price.​​​​​​​​b. ___$792,22______________

"monthly payment of $792.22"

c. Determine the finance charge.​​​​​​​​c. __$5069.92_______________

A = 792.22

n = 36

finance charge = total paid - amount to be financed

= 36*792.22 - 23450

= 5069.92

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} = 0[/tex]

[tex]\alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]

[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]

Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:

[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{1} = -2\cdot k[/tex]

[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{2} = -3\cdot k[/tex]

It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} + \alpha_{3} = 0[/tex]

[tex]3\cdot \alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

The set of vectors A and C are linearly independent.

Answer:

y= 250( 1-0.21)^x

Step-by-step explanation:

This represents exponential decay

The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.

The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that a population of 250 animals is decreasing at an annual rate of 21%.

p = a x b[tex].^t[/tex]

p = a x (1+r)[tex].^t[/tex]

p = 250 x (1+(-0.21))[tex].^t[/tex]

p = 250(0.79)[tex].^t[/tex]

Note that r = -0.21 is negative to indicate we have exponential decay.

Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.

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Step-by-step explanation:

a. The point estimate is the mean, 47 days.

b. The margin of error is the critical value times the standard error.

At 31 degrees of freedom and 98% confidence, t = 2.453.

The margin of error is therefore:

MoE = 2.453 × 10.2 / √32

MoE = 4.42

c.  The confidence interval is:

CI = 47 ± 4.42

CI = (42.58, 51.42)

d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.

e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.

Answer:

Margin of Error = ME =± 5.2592

Step-by-step explanation:

In the given question n= 20 < 30

Then according to the central limit theorem z test will be applied in which the standard error will be  σ/√n.

Sample Mean = μ = 64

Standard Deviation= S= σ = 12

Confidence Interval = 95 %

α= 0.05

Critical Value for two tailed test for ∝= 0.05 = ±1.96

Margin of Error = ME = Standard Error *Critical Value

ME = 12/√20( ±1.96)=

ME    = 2.6833*( ±1.96)= ± 5.2592

The standard error for this test is σ/√n

=12/√20

=2.6833

Answer:

1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70

2. Test Statistic : 0.54 , P value : 0.2946

3. Fail to reject null Hypothesis

4. No.

Step-by-step explanation:

1. Null hypothesis is 70% of children receive antibiotics.

Alternative hypothesis is more than 70% of children receive antibiotics.

2. Test statistic is calculated as;

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

z = [tex]\frac{0.01}{0.0185}[/tex]

z = 0.54

3. p value is calculated as;

1 - right tailed probability

1 - 0.7054 = 0.2946

Answer:

The fraction that this is true for = 7/13

Step-by-step explanation:

From the above question

Let the numerator be represented by a

Let the denominator be represented by b

If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

Cross Multiply

3(a + 5) = 2(b + 5)

3a + 15 = 2b + 10

Collect like terms

3a - 2b = 10 - 15

3a - 2b = -5..........Equation 1

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

Cross Multiply

4(a - 5) = 1(b - 5)

4a - 20 = b - 5

Collect like terms

4a - b = 20 - 5

4a - b = 15..........Equation 2

b = 4a - 15

3a - 2b = -5..........Equation 1

4a - b = 15..........Equation 2

Substitute 4a - 15 for b in equation 1

3a - 2b = -5..........Equation 1

3a - 2(4a - 15) = -5

3a - 8a + 30 = -5

Collect like terms

3a - 8a = -5 - 30

-5a = -35

a = -35/-5

a = 7

Therefore, the numerator of the fraction = 7

Substitute 7 for a in Equation 2

4a - b = 15..........Equation 2

4 × 7 - b = 15

28 - b =15

28 - 15 = b

b = 13

The denominator = b is 13.

Therefore,the fraction which this is true for = 7/13

To confirm

a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

7 + 5/ 13 + 5 = 2/3

12/18 = 2/3

Divide numerator and denominator by of the left hand side by 6

12÷ 6/ 18 ÷ 6 = 2/3

2/3 =2/3

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

7 - 5/13 - 5 = 1/4

2/8 = 1/4

Divide the numerator and denominator of the left hand side by 2

2÷2/8 ÷ 2 = 1/4

1/4 = 1/4

From the above confirmation, the fraction that this is true for is 7/13

Answer:

Spinner: 50%

Die: 50%

Step-by-step explanation:

Well for the spinner it depends on the amount of numbers it has,

in this case we’ll use 6.

So The probability of landing on the even numbers in a 6 numbered spinner.

2, 4, 6

3/6

50%

Your average die has 6 sides so the odd numbers are,

1, 3, 5

3/6

50%

Answer:

3+x

Step-by-step explanation:

sum= addition

a number= a number

Answer:

3+x  

eplanation                                  

Answer:

C.I =  0.7608   ≤ p ≤   0.8392

Step-by-step explanation:

Given that:

Let consider a  random sample n = 400 candidates where  320 residents indicated that they voted for Obama

probability [tex]\hat p = \dfrac{320}{400}[/tex]

= 0.8

Level of significance ∝ = 100 -95%

= 5%

= 0.05

The objective is to  develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.

The confidence internal can be computed as:

[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]

where;

[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960

SO;

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]

[tex]=0.8 \pm 1.960 \times 0.02}[/tex]

[tex]=0.8 \pm 0.0392[/tex]

= 0.8 - 0.0392     OR   0.8 + 0.0392  

= 0.7608    OR    0.8392

Thus; C.I =  0.7608   ≤ p ≤   0.8392

Answer:

C. It is one-half the area of a square of side length 4 units.

Step-by-step explanation:

Hey there!

Well if a square has side lengths of 4 units,

the area would be 16 because of l*w.

Now the formula for the area of a triangle is,

b*h/2

b = 4

h = 4

4*4=16

16 ÷ 2 = 8

So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,

meaning the area of a triangle is one-half the area of a square.

Hope this helps :)

Answer:

40091.

Step-by-step explanation:

Multiply 40.091 by 10 three times to get the answer.

40.091 * 10 = 400.91

400.91 * 10 = 4009.1

4009.1 * 10 = 40091.

The expression 40.091 x 10³ can be represented as 40091.

The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.

In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.

Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.

Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.

∴ The expression 40.091 x 10³ can be represented as 40091.

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Answer:

I NEED POINTS

Step-by-step explanation:

Answer:

Step-by-step explanation:

The claim: "Less than 40% of college students graduate with student loan debt."

The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%

If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.

A type I error occurs when the research rejects the null when it is actually true.

Answer:

6n=48

Step-by-step explanation:

product means multiplication

6×n=48

6n=48

An equation that shows this relationship is: A. 6n = 48.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;

6 × n = 48

6n = 48

n = 48/6

n = 8.

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Answer:

Hi! Answer will be below.

Step-by-step explanation:

The answer is 450.

If you divide 1.8 and 0.004 the answer you should get is 450.

Below I attached a picture of how to do long division...the picture is an example.

Hope this helps!:)

⭐️Have a wonderful day!⭐️

Answer:

Step-by-step explanation:

[tex] \mathrm{Given}[/tex],

[tex] \mathrm{Discount\% = 20\%}[/tex]

[tex] \mathrm{Marked \: price = 1250}[/tex]

[tex] \mathrm{Now \: let's \: find \: the \: discount \: amount}[/tex]

[tex] \mathrm{discount \: amount = dis\% \: of \: MP}[/tex]

[tex] \mathrm { = 20\% \: of \: 1250}[/tex]

[tex] \mathrm{ = 250}[/tex]

[tex] \mathrm{let's \: find \: the \: selling \: price}[/tex]

[tex] \mathrm{ = MP \: - \: discount \: amount}[/tex]

[tex] \mathrm{ = 1250 - 250}[/tex]

= $ [tex] \mathrm{1000}[/tex]

[tex] \mathrm{lets \: find \: the \: Vat \: amount}[/tex]

[tex] \mathrm{vat \: amount = vat\% \: of \: sp}[/tex]

[tex] \mathrm{ = 12.5\% \: of \: 1000}[/tex]

= $ [tex] \mathrm{ 125}[/tex]

[tex] \mathrm{Now \: finally \: let's \: find \: the \: selling \: price \: with \: vat}[/tex]

[tex] \mathrm{selling \: price \: + \: vat \: amount}[/tex]

[tex] \mathrm{ = 1000 + 125}[/tex]

= $ [tex] \mathrm{1125}[/tex]

Therefore, The final sale of the necklace is $ 1125

Hope I helped

Best regards!