A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Select one answer for question A, and select one answer for question B. B: (x+3)(x−3) B: (x+3i)(x−3i) B: (x−3i)(x−3i) B: (x+3)(x+3) A: x=3 or x=−3 A: x=3i or x=−3i A: x=3 A: x=−3i

Answer:

x = 3

Step-by-step explanation:

9x = 27

Divide both sides by 9,

x = 27/9 which on factorization of the numerator is written as

x = 9 x 3/9 = 3

Calculation 2: Exponent Or Index Method

9x = 27

Since 9 = 3² and 27 = 3³, the given equation takes the form

3² x = 3³

This gives

x = 3³ ÷ 3² = 3³­­­­­¯² [using the formula a^m ÷ a^n = a^(m-n)]

= 3¹ = 3 (since the first power of a number is the number itself)

9 x 1 = 9

9 x 2 = 16

9 x 4 = 36

We stop here because we have already got the answer 27, the right-side of the equality, when 9 is multiplied by 3 . So,

x = 3

hope this helped!

3s represents three times Sydney's age. Sydney's age is symbolized with an S.

Answer:

The answer is the first one on the bottom left.

Step-by-step explanation:

Answer: $264.54

Hope this helped! God bless!

Answer:

x(2x+3)

Step-by-step explanation:

Im guessing 2x2 is 2x^2

2x^2 + 3x = 0

x(2x+3)

Answer:

Mason reads the fastest

Answer:

c

Step-by-step explanation:

try to see how much every person reads every one or two minutes.

Charlie: 350 in two min

Mason :400 in two min

Sarah: 450 in two min (the middle of 300-600 is 450)

so between the three Sarah wins.

now Reilly is a bit more difficult but you can see that she read 4000 in 20 min. so if we divide it by 10 we can see she reads 400 in 2 min. and therefore Sarah os the winner.

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: family spending

X₁: income of a family

X₂: family size

X₃: additions to savings of a family

And the regression output (see attachment)

The population model is Y= α + β₁X₁ + β₂X₂ + β₃X₃

a)

To write the estimated regression equation of the relationship between the variables you have to use the information given in the regression output. Under the column "coefficients", the value that corresponds to "intercept" is the estimation of the y-intercept (a), the value under X₁ corresponds to the estimation for the slop for the variable "income of the family" (b₁), under X₂ is the estimation of the slope for the variable "family size" (b₂) and under X₃ is the estimation for the slope corresponding to the variable "additions to savings" (b₃)

The estimated regression equation is:

^Y= a + b₁X₁ + b₂X₂ + b₃X₃

^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃

b)

Using the SS information you can calculate the coefficient of determination as:

SStotal= SSReg+SSError= 45.9634+2.6218= 48.5852

[tex]R^2= \frac{SS_{Reg}}{SS_{Total}} = \frac{45.9634}{(48.5852)} = 0.946[/tex]

R²= 94.6%

This means that 94.6% of the variability of the average family spending is explained jointly by the family income, the family size and the addition to saving under the estimated model ^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃

c)

The hypotheses are:

H₀: β₁= β₂= β₃= 0

H₁: At least one βi≠0 ∀ i=1, 2, 3

α: 0.05

The statistic for the multiple regression is

[tex]F=\frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg};Df_{Error}}[/tex]

[tex]MS_{Reg}= \frac{SS_{reg}}{Df_{Reg}}= \frac{45.9634}{3} = 15.32[/tex]

[tex]MS_{Error}= \frac{SS_{Error}}{Df_{Error}} = \frac{2.6218}{11} = 0.238[/tex]

[tex]F_{H_0}= \frac{MS_{Reg}}{MS_{Error}}= \frac{15.32}{0.238}= 64.37[/tex]

p-value  < .00001

At a 5% significance level, there is enough evidence to reject the null hypothesis. This means that the family income, family size and the addition to savings modify jointly the average spending of families.

d.

Individual tests:

There are two possible statistics to test the significance of each independent variable: [tex]t= \frac{b_i-\beta_i }{S_{b_i}} ~~t_{n-3}[/tex] ∀ i= 1, 2, 3, or [tex]F=\frac{MS_{X_i}}{MS_{Error}} ~F_{Df_{X_i}; Df_{Error\\}}[/tex]

Since the output doesn't give us the information of the individual ANOVA, you have to use the t-test (Df: n-3= 12-3= 9) for these hypotheses. Using the p-value approach. the decision rule for the three hypothesis will be:

If p-value ≤ α ⇒ Reject null hypothesis.

If p-value > α ⇒ Do not reject the null hypothesis.

1)

H₀: β₁ = 0

H₁: β₁ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}= \frac{0.7992-0}{0.074}= 10.8[/tex]

p-value < .00001 ⇒ Decision is to reject the null hypothesis.

2)

H₀: β₂ = 0

H₁: β₂ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}= \frac{0.2280-0}{0.190}= 1.2[/tex]

p-value: 0.260773 ⇒ The decision is to not reject the null hypothesis.

3)

H₀: β₃ = 0

H₁: β₃ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}= \frac{-0.5796-0}{0.920}= -0.63[/tex]

p-value: 0.544355 ⇒ The decision is to not reject the null hypothesis.

So, at a 5% significance level, it seems that the three independent variables influence jointly the variation on the average spending of the families, but looking at them separately, only the income of the families seems to affect their spending habits significantly while the family size or their addition to savings don't seem to have major effect over their spending habits.

I hope this helps!

Answer:

[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]

[tex]Area\ of\ the\ garden\ =l1*b1[/tex]

Step-by-step explanation:

Let assume the l1 is the length of the garden and b1 is the breadth of garden then

[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]

Now,

[tex]Area\ of\ Garden\ = Length * Breadth[/tex]

[tex]Area\ of\ the\ garden\ =l1*b1[/tex]

Answer:

[tex]\frac{dV}{dt}[/tex]  = 1017.87 in³/min

[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min

Step-by-step explanation:

given data

radius r of a sphere is increasing at a rate = 3 inches per minute

[tex]\frac{dr}{dt}[/tex]  = 3

solution

we know volume of sphere is V = [tex]\frac{4}{3} \pi r^3[/tex]

so [tex]\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}[/tex]  

and when r = 9

so rate of change of the volume will be

rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)[/tex]

[tex]\frac{dV}{dt}[/tex]  = 1017.87 in³/min

and

when r = 37 inches

so rate of change of the volume will be

rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)[/tex]

[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min  

Answer:

Step-by-step explanation:

Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 0

σ = 1

the probability that a given score is less than negative 1.15 is expressed as

P(x < - 1.15)

z = (- 1.15 - 0)/1 = - 1.15

Looking at the normal distribution table, the probability corresponding to the z score is 0.13

P(x < - 1.15) = 0.13

The sketch of the region is shown in the attached photo

Answer:

73 mph

Step-by-step explanation:

The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).

We have that the model would be:

y = 43.81 - 0.395 * x

We need to solve for x, if y = 15

Replacing:

15 = 43.81 - 0.395 * x

Solving for x we have:

0.395 * x = 43.81 - 15

0.395 * x = 28.81

x = 28.81 / 0.395

x = 72.9

We are asked to round to the nearest number therefore x = 73.

The car will average 15 miles per gallon at the speed of 73 miles per hour.

Answer: (Multiply by 3)

63 pages in 3 hours

Step-by-step explanation:

Answer:

To go from 1 hour to 3 hours, you

✔ multiply by 3

.

Damian can read

✔ 63

pages in 3 hours.

Step-by-step explanation:

Answer:

0.00420 is the answer

Step-by-step explanation:

The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

The rounding number of 0.004198223 to 3 significant figures is 0.0042

Here,

The number is 0.004198223.

We have to find,  0.004198223 to 3 significant figures.

What is Rounding number?

Rounding means making a number simpler but keeping its value close to what it was.

Here,

The number is 0.004198223.

To find 3 significant figures,

We round a number to three significant figures in the same way that we would round to three decimal places.

Then, We count from the first non-zero digit for three digits. We then round the last digit.

Here, the digit is 9 then it will be round.

We get, the number is;

0.0042

We fill in any remaining places to the right of the decimal point with zeros.

So, The rounding number of 0.004198223 to 3 significant figures is 0.00420

Learn more about the rounding number visit:

https://brainly.com/question/4896544

#SPJ2

Answer:

Step 3

Step-by-step explanation:

The mistake was made in Step 3.

Step 1: Subtract the wholes. 4 - 1 = 3

Step 2: Subtract the fractions. 5/6 - 3/6 = 2/6

After Step 2, He should have added them instead of subtracting them:

3 + 2/6 = 3 2/6

So, step 3 was his mistake.

Answer:step 3

Step-by-step explanation: he should have added

Answer:

9.8

Step-by-step explanation:

updated

9^2=x^2+4^2

9*9=x*x+4*4

81=x*x-16

+16. +16

97=x*x

√97=√x*x

√97=x

So the answer is √97, but the question wants it rounded so it's actually 9.8

Answer:

The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:

[tex] z_{\alpha/2}= -1.64[/tex]

Step-by-step explanation:

[tex]n=8[/tex] the same size given

[te]\sigma[/tex] the population deviation is known

For this case we want to test if the population mean is less than 15 and that represent the alternative hypothesis and the complement would be the null hypothesis. So then the system of hypothesis are:

Null hypothesis: [tex]\mu \geq 15[/tex]

Alternative hypothesis:  [tex]\mu <15[/tex]

The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:

[tex] z_{\alpha/2}= -1.64[/tex]

Answer:

C

Step-by-step explanation:

2/3x - 5>3

Add 5 to each side

2/3x - 5+5>3+5

2/3x > 8

Multiply each side by 3/2

3/2 *2/3x > 8*3/2

x > 12

There is an open circle at 12 and the lines goes to the right

Answer:

(a) P(CBM) = 0.07

(b) P(not CBW) = 0.996

(c ) P(neither is color-blind) = 0.926

(d) P=(at least one is color-blind) = 0.074

Step-by-step explanation:

The correct data is  that Approximately 7% of American men and 0.4% of American women are red-green color-blind.

(a) Probability that he is red-green color-blind:

[tex]P(CBM) = 0.07[/tex]

(b) Probability that she is NOT red-green color-blind:

[tex]P(not\ CBW) =1- P(CBW)\\P(not\ CBW) = 1 -0.004\\P(not\ CBW) =0.996[/tex]

(c) Probability that neither are red-green color-blind

[tex]P(neither) = P(not\ CBW)*P(not\ CBM) \\P(neither) = 0.996 *(1-0.07)\\P(neither)=0.926[/tex]

(d) Probability that at least one of them is red-green color-blind

[tex]P(at\ least\ one) = 1- P(neither) \\P(at\ least\ one) = 1-0.926\\P(at\ least\ one) = 0.074[/tex]

Answer:

Step-by-step explanation:

a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.

b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.

c. Using three blocks: the completely randomized design experiment would be:

Donors younger than 30 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 30 to 59 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 60 and older:

Sent literature: Yes No

Contact by phone: Yes No

(Yes means yes to another donation and No means no to another donation)

Answer:

Step-by-step explanation:

a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.

b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.

c. Using three blocks: the completely randomized design experiment would be:

Donors younger than 30 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 30 to 59 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 60 and older:

Sent literature: Yes No

Contact by phone: Yes No

(Yes means yes to another donation and No means no to another donation)

Answer:

We can eliminate the second and third options because marking something up doesn't result in a number less than the original. Since we are told to select 3 options and there are 3 answer choices left we select the first, fourth, and fifth statements.

Answer:

= 19300

Step-by-step explanation:

Each claim consists of two parts = X + Y

where

X = the benefit that is paid to the surgeon and

Y = benefit that is paid to the hospital

V(X) = 5000, V(Y) = 10000 and V(X+Y) = 17000

So V(X+Y) = V(X) + V(Y) + 2cov(X,Y)

17000 = 5000 + 10000 +2 cov(X,Y)

17000 -15000 = 2cov(X,Y)

2000 = 2cov(X,Y)

cov(X,Y) = 1000

Now X is increased by flat Rs. 100 per claim and Y by 10% per claim

total benefit = X+100+Y+0.1Y = X+100 + 1.1Y

V(total benefit) = V(X) + 1.1²V(Y) +2(1.1)cov(X,Y) [ V(aX+bY)

= a²V(X) +b²V(Y) +2abcov(X,Y) and V(X+c) = V(X)]

= 5000 + (1.21*10000) + (2.2*1000)

= 5000 + 12100 + 2200

= 19300

Answer:

d. 102.3 units ^2

Step-by-step explanation:

Answer:

A meter is not part of the metric system. It's part of the U.S. customary system.

Answer:

Age difference between oldest the  youngest = 48 years

Step-by-step explanation:

Given: Ratio of ages of Kissi and Esinam is 3:5, ratios of ages of Esinam and Lariba is 3:5 and sum of the ages of all 3 is 147 years

To find: age difference between oldest the  youngest

Solution:

Let age of Lariba be x years

As ratios of ages of Esinam and Lariba is 3:5,

Age of Esinam = [tex]\frac{3}{5}x[/tex]  years

As ratio of ages of Kissi and Esinam is 3:5,

Age of Kissi = [tex](\frac{3}{5}) (\frac{3}{5}x)=\frac{9}{25}x[/tex] years

Sum of the ages of all 3 = 147 years

[tex]x+\frac{3}{5}x+\frac{9}{25}x=147\\ \frac{25x+15x+9x}{25}=147\\ x=\frac{147(25)}{49}=75[/tex]

Age of Lariba = x = 75 years

Age of Esinam = [tex]\frac{3}{5}(75)=45\,\,years[/tex]

Age of Kissi = [tex]\frac{9}{25}(75)=27\,\,years[/tex]

So,

Age difference between oldest the  youngest = 75 - 27 = 48 years

Answer:

{0, 1}

Step-by-step explanation:

Solving for 'x' in the inequality:

[tex]7x+3<17\\7x+3-3<17-3 \leftarrow \text{Subtraction Property of Equality}\\7x<14\\7x/7<14/7 \leftarrow \text{Division Property of Equality}\\\boxed{x<2}[/tex]

X's value has to be less than two to make the inequality true. So, {0, 1} should be the correct answer.

Answer:

I took the quiz and the answer is B

Step-by-step explanation:

Answer:

0.0178

Step-by-step explanation:

For computation of probability that all fourteen bets lose first we need to find out the Probability of losing in 1 bet is shown below:-

Probability of losing in 1 bet = 1 - P(winning)

= 1 - 0.25

= 0.75

With the help of probability of losing in 1 bet we can find out the Probability of losing in 8 bets which is here below:-

= Probability of losing in 1 bet ^ Number of loosing bets

= 0.75 ^ 14

= 0.017817948

or

= 0.0178

Therefore for computing the probability that all fourteen bets lose we simply applied the above formula.

Answer:

6.75 ft

Step-by-step explanation:

81 inches

We know there are 12 inches in 1 ft

81 inches * 1 ft/ 12 inches = 81/12 ft =6.75 ft

Answer:

20:30 goes to 8:12

the rest goes to 6:18

Step-by-step explanation:

i may be wrong

Answer:

7:12 is equivalent to 6:18

20:30 is equivalent to 8:12

5:15 is equivalent to 6:18

Step-by-step explanation:

plz mark brainliest

Answer:

170m

Step-by-step explanation:

The answer to the above question is letter d which is 170 m. To get the 170 m, kindly check the below solution: 

x^2 + 13x = 1764 so x = -49 and 36, we take 36 as its the positive value. And the other side is 49. Now use 2(l+b) to find perimeter. You get (36+49)*2 = 170

Answer:

x = 54°

h = 7.5cm

w= 6cm

Step-by-step explanation:

Find attached the diagrams as found at Maths made easy.

Similar shapes have same shapes but different sizes.

When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.

B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A

To determine the value of x, h and w, let's look at the relationship of A and B.

h = 1.5 × 5cm

h = 7.5cm

9cm = 1.5 × w

w = 9cm/1.5

w= 6cm

Since the angles do not change when a shape is enlarged, the value of x = 54°

x = 54°