Translate this sentence into an equation. 43 is the sum of 11 and Carlos age. Use the variable c to represent Carlos age.

Answer:

0.2207

Step-by-step explanation:

Here, we want to find the probability that the sample mean is greater than 25.

What we use here is the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question;

x = 65, mean = 63, SD = 13 and n = 25

Plugging these values in the z-score equation, we have

Z-score = (65-63)/13/√25 = 2/13/5 = 0.77

So the probability we want to calculate is ;

P(z > 0.77)

This can be obtained from the standard normal distribution table

Thus;

P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p

Answer:

86.28 ft²

Step-by-step explanation:

The figure given consists of a rectangle and a semicircle.

The area of the figure = area of rectangle + area of semicircle

Area of rectangle = [tex] l*w [/tex]

Where,

l = 10 ft

w = 8 ft

[tex] area = l*w = 10*8 = 80 ft^2 [/tex]

Area of semicircle:

Area of semicircle = ½ of area of a circle = ½(πr²)

Where,

π = 3.14

r = ½ of 8 = 4 ft

Area of semi-circle = ½(3.14*4) = 6.28 ft²

Area of the figure = area of rectangle + area of semi-circle = 80 + 6.28 = 86.28 ft² (nearest hundredth)

Answer:

the area of the figrue is 105.12

Step-by-step explanation:

Answer:

1/2 to the power of 3= 1/8

Step-by-step explanation:

1/2*1/2=1/4

1/4*1/2=1/8

d?

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(\dfrac{1}{2})^3}[/tex]

[tex]\mathsf{= \dfrac{1}{2}^3}[/tex]

[tex]\mathsf{= \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}}[/tex]

[tex]\mathsf{= \dfrac{1 \times 1 \times 1}{2 \times 2 \times 2}}[/tex]

[tex]\mathsf{\mathsf{= \dfrac{1 \times 1} {4 \times 2}}}[/tex]

[tex]\mathsf{= \dfrac{1}{8}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D.\ \dfrac{1}{8}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

P(1 |F) = 10/17

Step-by-step explanation:

Let events

1 = restaurant 1

2 = restaurant 2

F = full-time worker chosen

P = part-time worken chosen

P(1 and F) = 1/2 * 10/16 = 5/16

P(2 and F) = 1/2 * 7/16 = 7/32

P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32

P(1 | F)          Probability of choosing restaurant 1 given a full-time was chosen

= P(1 and F) / P(F)

= 5/16  / (17/32)

= 5/16 * 32/17

= 10 / 17

Answer:

symmetric

Step-by-step explanation:

it kind of evenly falls to the left and right from the highest value in the middle

skewed would be different and would look like a straight line not a quadratic equation

Answer:

[tex]x> \frac{8}{51} [/tex]

Step-by-step explanation:

[tex]7x - \frac{5}{8} x + 3>4[/tex]

Bring constants to one side, simplify:

[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]

*Note that the inequality sign only changes when you divide the whole inequality by a negative number.

Answer:

[tex]x>\frac{8}{51}[/tex]

Step-by-step explanation:

[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]

I hope it helps :)

Answer:

FH = 134

Step-by-step explanation:

From the question given:

G is the midpoint of FH

FG = 14x + 25

GH = 73 - 2x

FH =?

Next, we shall determine the value of x. The value of x can be obtained as follow:

Since G is the midpoint of FH, this implies that FG and GH are equal i.e

FG = GH

With the above formula, we can obtain the value of x as follow:

FG = 14x + 25

GH = 73 - 2x

x =?

FG = GH

14x + 25 = 73 - 2x

Collect like terms

14x + 2x = 73 - 25

16x = 48

Divide both side by 16

x = 48/16

x = 3

Next, we shall determine the value of FG and GH. These can be obtained as shown below:

FG = 14x + 25

x = 3

FG = 14x + 25

FG = 14(3) + 25

FG = 42 + 25

FG = 67

GH = 73 - 2x

x = 3

GH = 73 - 2x

GH = 73 - 2(3)

GH = 73 - 6

GH = 67

Finally, we shall determine FH as follow:

FH = FG + GH

FG = 67

GH = 67

FH = FG + GH

FH = 67 + 67

FH = 134

Therefore, FH is 134

Answer:

The answer is "253"

Step-by-step explanation:

In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:

Given:

[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]

[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]

integrate the above value:

[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]

When the value of n=1 then t=0

[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]

so the value of  n is:

[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]

when we put the value t= 15 then,

[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]

Answer:

A. 418, 418

Step-by-step explanation:

The formula to convert miles to meters is the following:

1 = 1,609.34

so for every 1 mile, you have 1,609.34 meters

so you take your distance in miles and multiply it by 1,609.34

d= 260 x 1,609.34

d = 418, 428.4

Answer:

2 ( x+4) ( x+1)

Step-by-step explanation:

2x^2+10x+8

Factor out 2

2 ( x^2 +5x+4)

What two numbers  multiply to 4 and add to 5

4*1 = 4

4+1 = 5

2 ( x+4) ( x+1)

[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]

By middle term factorisation,

⇛ 2x² + 2x + 8x + 8

⇛ 2x(x + 1) + 8(x + 1)

⇛ (2x + 8)(x + 1)

⇛ 2(x + 4)(x + 1)

☃️ Now you can break it down and check which are the factors of the polynomial according to options.

━━━━━━━━━━━━━━━━━━━━

Answer: Midline equation: y = -7

Step-by-step explanation: This function is a sinusoidal function of the form:

y = a.cos(b(x+c))+d

Midline is a horizontal line where the function oscillates above and below.

In the sinusoidal function d represents its vertical shift. Midline is not influenced by any other value except vertical shift. For that reason,

Midline, for the function: [tex]h(x) = -4cos(5x-9) - 7[/tex] is y=d, i.e., [tex]y=-7[/tex]

Answer:

y=-7

Step-by-step explanation:

Answer: Yes

Explanation: Yes because, sometimes you need to do stuff to get things of your head

Answer:

The probability that the selected adult has liver problems is 0.08

Step-by-step explanation:

In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.

Let E(L) be the event that an adult has liver problems.

The probability is directly obtainable from the question and it is given as 8%

Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08

Answer:

 $900

Step-by-step explanation:

To begin with let us estimate the total cash value of the prices

$1000 x 1= 1000

$500 x 1=  500

$50 x 2= 100

Total = $1600

Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets

2.5*1000= $2,500

Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600

Then the expected profit is = $2,500-$1600= $900

Answer:

6/50

Step-by-step explanation:

There are 50 tiles

6 purple

18 pink

26 orange

P( purple) = purple/ total

                = 6/50

Answer:

The correct option is (b) 0.3333.

Step-by-step explanation:

The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].

The standard error is given as follows:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]

Compute the standard deviation of the sample mean as follows:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

    [tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]

Thus, the standard deviation of the sample mean is 0.3333.

Answer:

8

Step-by-step explanation:

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

8x→1

7y→1

The largest exponent is the degree of the polynomial.

1

The leading term in a polynomial is the term with the highest degree.

8x

The leading coefficient of a polynomial is the coefficient of the leading term.

____________________________________________________________

The leading term in a polynomial is the term with the highest degree.

8x

The leading coefficient in a polynomial is the coefficient of the leading term.

8

List the results.

Polynomial Degree: 1

Leading Term: 8x

Leading Coefficient: 8

Hope This Helps!!!

Answer:

AB = 16 Units

Step-by-step explanation:

In the given figure, CD is the diameter and AB is the chord of the circle.

Since, diameter of the circle bisects the chord at right angle.

Therefore, AE = 1/2 AB

Or AB = 2AE...(1)

Let the center of the circle be given by O. Join OA.

OA = OD = 10 (Radii of same circle)

Triangle OAE is right triangle.

Now, by Pythagoras theorem:

[tex] OA^2 = AE^2 + OE^2 \\

10^2 = AE^2 + 6^2 \\

100= AE^2 + 36\\

100-36 = AE^2 \\

64= AE^2 \\

AE = \sqrt{64}\\

AE = 8 \\

\because AB = 2AE..[From \: equation\: (1)] \\

\therefore AB = 2\times 8\\

\huge \purple {\boxed {AB = 16 \: Units}} [/tex]

Answer:

[tex]\sqrt{85}[/tex].

Step-by-step explanation:

[tex]x[/tex]-coordinates:

[tex]y[/tex]-coordinates:

Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:

Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)

[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].

Answer:

C

Step-by-step explanation:

Answer:

B. 259

Step-by-step explanation:

6^(i - 1) for i = 1 to 4

sum = 6^(1 - 1) + 6^(2 - 1) + 6^(3 - 1) + 6^(4 - 1) =

= 6^0 + 6^1 + 6^2 + 6^3

= 1 + 6 + 36 + 216

= 259

Answer: B. 259

Answer:

A

Step-by-step explanation:

congruent means they have the same shape and size. hope this helps :)

Answer:

We conclude that the population mean is equal to 490.

Step-by-step explanation:

We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490      {means that the population mean is equal to 490}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490     {means that the population mean is different from 490}

The test statistics that will be used here is 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_1_4[/tex]

where, [tex]\bar X[/tex] = sample mean = 495

            s = sample standard deviation = 9

             n = sample of observations = 15

So, the test statistics =   [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                     =  2.152

The value of t-test statistics is 2.152.

Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 490.

Answer:

6 years

Step-by-step explanation:

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:

[tex]y=ab^x[/tex]

Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8

[tex]y=ab^x\\8=ab^0\\a=8[/tex]

Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2

Therefore:

[tex]y=ab^x\\y=8(1.2^x) \\[/tex]

To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x

[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]

x = 6 years to the nearest year

Answer:

5 years

Step-by-step explanation:444

Answer:

170

Step-by-step explanation:

3(4)³ - 2(4)² + 10

192 - 32 + 10 = 170

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

   Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\frac{(17)(3.141593)}{12}[/tex]

= [tex]\frac{53.407075}{12}[/tex]

= [tex]4.45059[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

If this helped you, could you maybe give brainliest..?

Also Have a great day/night!

❀*May*❀

I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.

Answer:

x >162

Step-by-step explanation:

x+54 > 216

Subtract 54 from each side

x+54-54 > 216 - 54

x >162

Answer:

[tex]\huge \boxed{{x>162}}[/tex]

Step-by-step explanation:

[tex]x+54 > 216[/tex]

[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]

[tex]x+54 -54> 216-54[/tex]

[tex]x>162[/tex]

Answer:

c. It does not appear to be within statistical control because there is an upward trend.

Step-by-step explanation:

Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.

13226/29= 456.068965517

Answer:

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

Step-by-step explanation:

We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.

Ages                Frequency

18 to 20             4.2

21 to 24             7.8

25 to 34           20.8

35 to 44           23.7

45 to 64           50.1

65 and over       28.2

∑                        134.8

The probability of an event is given by the occurrence of an event by the total occurrences .

So

Here the occurrence of ages 18-20 is given by 4.2

and the total frequency is 134.8

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

1. Not binomial: there are more than two outcomes for each trial.

Thus, option (B) is correct.

2. Procedure results in a binomial distribution.

Thus, option (B) is correct.

1. Not binomial: there are more than two outcomes for each trial.

In a binomial distribution, each trial can have only two outcomes (usually referred to as success and failure).

In this case, the procedure involves rolling a single die 53 times and keeping track of the "fives" rolled.

Since the outcome can be any number from 1 to 6 on each trial, it does not meet the criteria for a binomial distribution.

Thus, option (B) is correct.

2. Procedure results in a binomial distribution.

In this case, the procedure involves spinning a roulette wheel 7 times and keeping track of the winning numbers. The outcome of each trial is either a win or a loss, which satisfies the requirement for a binomial distribution.

Thus, option (B) is correct.

Learn more about Binomial Distribution here:

https://brainly.com/question/29163389

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