What’s the correct answer for this question?

Answer:

The time (t) = 2.6 years

Step-by-step explanation:

To calculate the time for earning a compound interest, compounded on a certain amount of present value (PV), compounded periodically, the following formula is used:

[tex]FV=PV(1+\frac{i}{n} )^{n*t}[/tex]

where:

FV = future value = $6,100

PV = present value = $5,000

i = interest rate in decimal = 7.5% = 0.075

n = number of compounding periods per year = quarterly = 4 (4 quarters a year)

t = time of compounding in years = ???

Therefore the time is calculated thus:

[tex]6100=5000(1+\frac{0.075}{4} )^{4*t}[/tex]

[tex]6100=5000(1+0.01875 )^{4t}[/tex]

[tex]6100=5000(1.01875 )^{4t}[/tex]

Next, let us divide both sides of the equation by 5000

[tex]\frac{6100}{5000} = \frac{5000(1.01875)^{4t} }{5000}[/tex]

1.22 = [tex](1.01875)^{4t}[/tex]

Taking natural logarithm of both sides

㏑(1.22) = ㏑[tex](1.01875)^{4t}[/tex]

㏑(1.22) = 4t × ㏑(1.01875)

0.1989 = 4t × 0.01858

4t = [tex]\frac{0.1989}{0.01858} = 10.71[/tex]

∴ 4t = 10.71

t = 10.71 ÷ 4 = 2.6 years

Step-by-step explanation:

(116-718) /(2.805+118) [as, there cannot be two decimals in one numbers

=-602/120.805

=0.498

Answer:

3 yards

Step-by-step explanation:

Divide inches by 36

[tex]108/36\\=3yards[/tex]

Answer:

[tex]3 \: \: yards[/tex]

Step-by-step explanation:

[tex]1 \: \: yard = 36\: \: inches \\ yard \: \: x = 108 \: \: inches[/tex]

So,

[tex] 1 = 36 \\ x = 108 \\ \\ cross \: \: \: multiple \\ \\ 108 = 36x \\ \frac{108}{36} = \frac{36x}{36} \\ x = 3 \: \: yards[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

Hello!

Given the  variables:

Y: Blood pressure of a hospital patient (mmHg)

X: Age of a patients (years)

You have to analyze the claim that the rising numbers in high blood pressure related deaths is associated with the aging of the State's population.

i)

[tex]r= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{\sqrt{[sumX^2\frac{(sumX)^2}{n} ]+[sumY^2-\frac{(sumY)^2}{n}] } }[/tex]

To calculate the correlation coefficient you need to do several additional calculations.

n= 10

∑Y= 1005 mm Hg; ∑Y²= 106475 mmHg²

∑X= 360 years; ∑X²= 16500 years²

∑XY= 40425 years*mmHg

[tex]r= \frac{40425-\frac{360*1005}{10} }{\sqrt{[16500\frac{(360)^2}{10} ]+[106475-\frac{(1005)^2}{10}] } }= 0.96[/tex]

The coefficient of correlation is close to 1 and positive, this means that there is a strong positive correlation between these two variables. This means the blood pressure increases as age does.

ii)

If blood pressure increases with age and so does the risk of dying due to a high blood pressure, then the most logical decision to take is to give priority to the old adults.

iii)

The estimated regression is ^Y= a + bXi + ei

a= y-intercept: is the estimated average blood pressure of the patients when age is 0 years.

b= slope: in the modification of the estimated average blood pressure of the patients when age increases 1 year.

ei= residues

The estimated regression model will allow you to analyze and predict the values of blood pressure of patients within the determined range of age.

iv)

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{40425-\frac{360*1005}{10} }{16500-\frac{(360)^2}{10} } = 1.20 \frac{mmHg}{years}[/tex]

X[bar]= 36 years

Y[bar]= 100.50 mmHg

[tex]a= Y[bar] - bX[bar]= 100.50-1.20*36= 57.33 mmHg[/tex]

The estimated regression equation is ^Y= 57.33 + 1.20Xi

57.33mmHg in the estimated average blood pressure of a patient age zero.

1.20 mmHg/years is the modification on the estimated average blood pressure when the age of the patients increases one year.

v)

At birth an infant is zero years old, so according to the regression model, it's blood pressure will be 57.33 mmHg

According to medical parameters 64.41 mmHg is the average blood pressure of a newborn child, as you can see this model is a little off the average but still within acceptable parameters.

vi)

Using the estimated regression equation you can predict the value of blood pressure for a determined age by replacing the value of X in it:

^Y= 57.33 + 1.20*90= 165.33 mmHg

It is predicted that a 90-year-old patient will have a blood pressure of mmHg.

vii)

[tex]R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{sumY^2-\frac{(sumY)^2}{n} } = \frac{1.20^2[16500-\frac{(360)^2}{n} ]}{[106475-\frac{(1005)^2}{10} ]} = 0.93[/tex]

93% of the variability of the patients blood pressure is explained by their age under the model:  ^Y= 57.33 + 1.20Xi

I hope this helps!

Answer:

quartic

Step-by-step explanation:

p(x) = 7 x^3 + 2 x^2 - 3 x^4

The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 3, 2, and 4.

The degree of the polynomial is the highest degree of any of the terms; in this case, it is 4.

Answer:

Step-by-step explanation:

Given that:

[tex]\mathbf{H_o : \sigma = 140} \\ \\\mathbf{H_i : \sigma > 140} \\ \\ \mathbf{ \alpha = 0.05 \ \ \ \ n = 25 \ \ \ \ S = 150}[/tex]

1. This type of test is right tailed since the alternative hypothesis is right tailed

2. The Observed test statistic is calculated as follows:

[tex]X^2 = \dfrac{(n-1)s^2}{\sigma^2} \\ \\ X^2 = \dfrac{(25-1)150^2}{140^2} \\ \\ X^2 = \dfrac{(24)22500}{19,600} \\ \\ X^2 =27.55[/tex]

3. Critical Value

where ∝ = 0.05 and the test statistic is right tailed ;

By using [tex]X^2[/tex]   table

[tex]X^2 _{\alpha/2 , n-1}= 36.415[/tex]

4. Conclusion:

∝ = 0.05

where

X² = 36.415

Therefore ; we reject [tex]\mathbf{H_o}[/tex]

Answer:

Hai

It should be the fourth option. 44/20<45/20

Because firstly we should bring them same to make calculation.

im bringing them denominator to 20.

for 11/5, i should multiply both with 4.

11×4 = 44/20 = 5 × 4

for 9/4 ill multiply both with 5.

9×5 = 45/20 = 5 × 4

good luck(:

Answer:Y=x3

2nd answer: Just add it all up and divide by how many things you had to add. For an example: (2+2+2+2)/4.

Step-by-step explanation:

Answer:

B. h=S/πr²

Step-by-step explanation:

The question lacks options. Here is the complete question.

Which of the following equations is equivalent to S = πr²h

a. h=S-πr^2

b. h=S/πR^2

C. h= πr^2/S

D. h=S+ πr^2

To know the equation equivalent to πr²h, we will make h the subject of the formula as shown from the one given in equation.

S = πr²h

To get h, we will divide both sides by the coefficient of h (i.e πr²)

S/πr² = πr²h/πr²

S/πr² = h

h = S/πr²

This shows that h = S/πr² is equivalent to S = πr²h

Answer:

I would recommend optimum number of six segments for each arc.

Step-by-step explanation:

The optimum number of segments I would recommend for each arc is six. This way, the circle interpolation will divide the arc into six segments, and approximating each segment by a straight line.

Answer:

Step-by-step explanation:

Brazil : 12,500,000 = 5,000,000 + 5,000,000 + 2,500,000

                               = full cat + full cat  + half cat

Answer:

Answers are below

Step-by-step explanation:

The center coordinates of the circle are at (0,0).

The radius of the circle is 20

I graphed the circle on the graph below to show you how I got my answers.

The center of the equation x² + y² = 400 is, (0, 0).

And, The radius is 20.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The equation is,

⇒ x² + y² = 400

Now, We know that;

The standard for of the equation of circle is,

⇒ (x - h)² + (y - k)² = r²

Where, (h, k) is the center of the circle and 'r' is the radius of the circle.

Hence, By comparing we get;

⇒ x² + y² = 400

⇒ (x - 0)² + (y - 0)² = 20²

The center of the equation x² + y² = 400 is, (0, 0).

And, The radius is 20.

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Answer:

A

Step-by-step explanation:

multiply 7/8 by 2/2 to get 14/16. they are equal

Answer:

Option (1).

Step-by-step explanation:

Amount of water hold by both the pitchers (Large + small) = 12 cups

Let the small pitcher holds the water = S cups

If the water hold by the large pitcher is twice the size of the small pitcher, then the amount of water hold by large pitcher = 2S

Total amount water hold by both = S + 2S

Equation for this situation will be,

S + 2S = 12

Therefore, Option (1) will be the answer.

Answer:

Option C is correct.

Alex earned about $60 more than Joaquin did.

Step-by-step explanation:

The linear regression equation

y = 0.18 x + 320.22

is used to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise.

Joaquin sold $1500 worth of goods. Meaning that x for that week for Joaquin is 1500.

Joaquin' s salary for that week is then given as

y = 0.18x + 320.22

y = 0.18(1500) + 320.22 = 590.22

Hence, Joaquin's salary for that week = $590.22

Alex earns $650 that week. Meaning that y for Alex in that week = 650

y = 0.18x + 320.22

650 = 0.18x + 320.22

0.18x = 650 - 320.22 = 329.78

x = (329.78/0.18) = 1832.1

Hence, Alex sold goods worth $1832.1 that week.

Joaquin sold goods worth $1500

Joaquin earned $590.22

Alex sold goods worth $1832.1

Alex earned $650

From this calculation, it is evident that 'Alex earned about $60 more than Joaquin did' is the correct option as $650 is about $60 more than $590.22

Hope this Helps!!!

Answer:

the answer is C :)

Step-by-step explanation:

Answer:

D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data

Step-by-step explanation:

One easy way we can easily tell about the spread and variation data sets is by considering the length of the box in the box plot.

The length of a box plot represents the interquartile range of a data set. The longer the box length, the more the variation and spread there is in the data.

Therefore, considering the diagram of the box plots attached below, the box length for length of boys at 24months is longer than that of the box length of heights of boys at 12 months.

The longer box lengths for heights of boys at 24 months indicates a larger interquartile range compared to that of heights of boys at 12 months. This larger interquartile range implies that, there is more variation in heights at 24 months.

Therefore, the correct option is "D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data."

Answer:

[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm

Step-by-step explanation:

Information provided

[tex]\bar X=2941[/tex] represent the sample mean

[tex]s=12[/tex] represent the standard deviation

[tex]n=25[/tex] sample size      

[tex]\mu_o =2944[/tex] represent the value to test

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

t would represent the statistic

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

Hypothesis to test

We want to test if the true mean for this case is equal to 2944 mm, the system of hypothesis would be:      

Null hypothesis:[tex]\mu = 2944[/tex]      

Alternative hypothesis:[tex]\mu \neq 2944[/tex]      

The statistic for this case would be given by:

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

Replacing the info given we got:

[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]  

Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm

Answer:

A. Step 2

Step by step explanation:

It was applied in Step 2 where 9 was added to both sides of the equation.

Answer:

The point estimate is 0.3488.

The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).

Step-by-step explanation:

In a sample with a number n of people surveyed with a point estimate of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1078, \pi = \frac{376}{1078} = 0.3488[/tex]

The point estimate is 0.3488.

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 - 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3114[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 + 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3862[/tex]

The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).

Answer: B C E

Step-by-step explanation:

Answer:

D. (X + 3 ) ( X +1 )

process:

x² + 4x + 3

= x² + (3 + 1)x +3

= x² + 3x + x + 3

= X (x+3) + 1 (X+3)

= (X + 3 ) ( X +1 )

Answer:

-7 goes in the box

Step-by-step explanation:

x^ -3 = x^4 * x^n

We know that a^b * a^c = a^ (b+c)

x^-3 = x^(4+n)

When the bases are the same the exponents are the same

-3 = 4+n

Subtract 4 from each side

-3 -4 = 4+n-4

-7 = n

Answer:

car = 1.1 mi/min

bus = 1.05 mi/min

car travels faster

Step-by-step explanation:

recall that speed is given by the gradient (i.e slope) of a distance vs time graph or equation.

for the car:

equation is y = 1.1x

recall that for an equation in the form y = mx + b, slope = m

if we compare the given equation to the general equation, it is clear that

speed of car = slope = m = 1.1 miles/min  (answer)

for the bus,

we are given 2 points (2,2.1) and (4,4.2)

if we apply the formula for slope (see attached for reference)

slope, m

= (4.2 - 2.1) / (4 - 2)

= 2.1 / 2

= 1.05 mi/min= speed of bus (answer)

comparing the 2 speeds, we can see that the car has the higher speed (travels faster).

Answer:

Car:1.1

Bus:1.05

Car is going faster.

Step-by-step explanation:

This is right. I got it right on Big Ideas Math (Pre-Algebra)

Answer:

Step-by-step explanation:

The standard error of the mean is defined as the ratio of standard deviation to the square root of the sample size of a data. The standard error of the mean is mathematically expressed as shown below;

[tex]X = \frac{\sigma}{\sqrt{n} }[/tex]

X is the standard error of the mean

[tex]\sigma[/tex] is the standard deviation

n is the sample size.

Given;

[tex]\sigma = 121\\n = 256[/tex]

On substitution into the formula we have;

[tex]X = \frac{121}{\sqrt{256} }[/tex]

[tex]X = \frac{121}{16} }\\[/tex]

X ≈ 7.56

Step 1:

Convert the electricity per hour in kilowatts,

Electricity per hour = 20 watts

=20/1000 kilo,watts

Step 2:

The electricity consumes in 5 hour is ,

Electricity in 5 hour = 5x 20/1000 kilo watts.

Obtain the cost as,

=5x20/1000x10

=1 Cent

Answer: =1 Cent

Please mark brainliest

Hope this helps.

The cost of the energy consumed by the laptop for the 5 hours period is 5 cents.

Given:

rate of energy consumption of the laptop, R = 20 Watts per hour

time of operation of the laptop, t = 5 hours

cost of energy consumption, c = 10 cent per kWh

To find:

The energy consumed by the laptop in kWh is calculated as;

[tex]Energy = Power \times time \\\\Energy = (\frac{20 \ W}{hr} \times 5 \ hr) \times 5\ hr\\\\Energy = (100 \ W) \times ( 5 \ hr)\\\\Energy = (0.1 \ kW) \times (5 \ hr)\\\\Energy = 0.5 \ kWh[/tex]

The cost of consuming 0.5 kWh is calculated as;

[tex]Cost = energy \ rate \ \times \ energy \ consumed \\\\Cost= \frac{10 \ cent}{kWh} \times 0.5 \ kWh\\\\Cost = 5 \ cents[/tex]

Thus, the cost of the energy consumed by the laptop for the 5 hours period is 5 cents.

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Answer:

Correct answer is C. (15,6)

Step-by-step explanation:

Let us think of the [tex]xy[/tex] co-ordinates plane. We can move in four directions.

1. North (i.e. upwards) If we move north or upwards the value of y-coordinate  will increase.

2. South (i.e. downwards) If we move south or downwards the value of y-coordinate will decrease.

3. West (i.e. left) If we move west or left the value of x-coordinate will decrease.

4. East (i.e. right) If we move east or right the value of x-coordinate will increase.

Let us imagine, the starting coordinate of Tara be [tex](x,y)[/tex]

Let us apply the above 4 directions and the properties in the question statement.

Step 1: Tara walks 4 blocks west (left), x coordinate will decrease by 4.

New coordinates will be [tex](x-4,y)[/tex].

Step 2: Tara walks 3 blocks north (up), y coordinate will increase by 3.

New coordinates will be [tex](x-4,y+3)[/tex].

Step 3: Tara walks 2 blocks west (left), x coordinate will decrease by 2.

New coordinates will be [tex](x-4-2,y+3) \Rightarrow (x-6,y+3)[/tex].

Now Tara is at (9,9)

Comparing the x and y coordinates:

[tex]x-6=9\\\Rightarrow x = 15[/tex]

[tex]y+3=9\\\Rightarrow y = 6[/tex]

So, Tara's starting point is (15,6) hence, option C is correct.

Answer:

1.75x ≤ 25

Step-by-step explanation:

Answer:

To the nearest tenth of a degree

∠E= 47.9°

Step-by-step explanation:

ΔDEF , let's recognize that it's a right angle triangle because of the presence of ∠F=90°.

Other important measurements are

DE = 82 feet, and EF = 55 feet.

We are to find ∠E

Let's find the missing side first

Side DF

DF² = DE² - EF²

DF²= 82²_55²

DF²=6724-3025

DF²= 3699

DF= 60.82 feet

Let's use the sine formula to look for the angle.

DF/sin ∠E= DE/sin 90

Sin 90= 1

DE= 82

DF= 60.82

Sin ∠E= DF/DE

Sin ∠E= 60.82/82

Sin ∠E= 0.7417

∠E= sin^-1 (0.7417)

∠E= 47.8764

To the nearest tenth of a degree

= 47.9°