A polynomial function has a root of -6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2, and a
root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about
the graph is true?
O The graph of the function is positive on (-6, -2).
O The graph of the function is negative on (-0, 0).
O The graph of the function is positive on (-2, 4).
O The graph of the function is negative on (4.co).

Answer:

The solution to the equation  log3(x+2)=1 is given by x=1

Step-by-step explanation:

We are given that

[tex]log_3(x+2)=1[/tex]

We have to find the graph which shows the  solution to the equation log3(x+2)=1.

[tex]log_3(x+2)=1[/tex]

[tex]x+2=3^1[/tex]

Using the formula

[tex]lnx=y\implies x=e^y[/tex]

[tex]x+2=3[/tex]

[tex]x=3-2[/tex]

[tex]x=1[/tex]

Answer:

[tex]y = - \frac{1}{3}x + 5[/tex]

Step-by-step explanation:

Consider two points through which the line passes.

Let it be ( 0 , 5 ) and ( 6 , 3 )

Step 1 : Find slope

    [tex]Slope, m = \frac{y_2 - y_ 1 }{x_2 - x_1}[/tex]

                 [tex]= \frac{3-5}{6-0} \\\\=\frac{-2}{6}\\\\= -\frac{1}{3}[/tex]

Step 2 : Find the equation of the line passing through the points.

       [tex]( y - y_1) = m (x - x_1)\\\\(y - 5) = -\frac{1}{3} ( x - 0) \\\\y = -\frac{1}{3}x + 5[/tex]

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Answer:

  S = {2, 3, 5, 7, 11, 13}

  2^6 = 64 subsets

Step-by-step explanation:

The list of primes less than 15 is ...

  S = {2, 3, 5, 7, 11, 13}

__

A set with n unique elements has 2^n unique subsets, including the empty set and the full set. This set of 6 elements has 2^6 = 64 subsets.

Answer:

The  weight that separate the top 8% by 5.2605 and the weight that separate bottom 8% by 5.1195.

Step-by-step explanation:

We are given that

Mean,[tex]\mu=5.19[/tex]

Standard deviation,[tex]\sigma=0.05[/tex]

We have to find the two weights that separate the top 8% and the bottom 8%.

Let x1 and x2 the two weights that separate the top 8% and the bottom 8%.

Z-value for p-value =0.08 =[tex]-1.41[/tex]

For 8% bottom

[tex]Z=\frac{x_1-\mu}{\sigma}=-1.41[/tex]

[tex]\frac{x_1-5.19}{0.05}=-1.41[/tex]

[tex]x_1-5.19=-1.41\times 0.05[/tex]

[tex]x_1=-1.41\times 0.05+5.19[/tex]

[tex]x_1=5.1195[/tex]

For 8% top

p-Value=1-0.08=0.92

Z- value=1.41

Now,

[tex]\frac{x_2-5.19}{0.05}=1.41[/tex]

[tex]x_2-5.19=1.41\times 0.05[/tex]

[tex]x_2=1.41\times 0.05+5.19[/tex]

[tex]x_2=5.2605[/tex]

(x1,x2)=(5.1195,5.2605)

Answer:

15×115+3{0÷3}5-3×(-6)

15×115+3of 0 of 5-3×(-6)

15×115+0 of 5-3×(-6)

15×115+0+18

1725+0+18

1743

Answer:

5^2×5

=25×5

=125

hope this will help you

Answer:

125

Step-by-step explanation:

hope this helps you

=25×5

=125

Answer:

n=-9,-8,-7

Step-by-step explanation:

n<100

but that is the positive square root

\(-10 n is between the negative and positive square root of 100

thus, n=-9,-8,-7

The solution of the inequality n² < 100 will be less than 10.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The inequality is given below.

n² < 100

Simplify the equation, then we have

n² < 100

n² < 10²

n < 10

The solution of the inequality n² < 100 will be less than 10.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

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Answer:

  29.4 m/s

Step-by-step explanation:

Speed is proportional to time, so we have ...

  speed / time = s/3 = 49/5

  s = 3/5(49) = 29.4

The speed of the object is 29.4 m/s after 3 seconds.

Answer:

6/11, 11/2, 5.77, 5.772

Step-by-step explanation:

Answer:

0.64 = 64% probability that the student passes both subjects.

0.86 = 86% probability that the student passes at least one of the two subjects

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Passing subject A

Event B: Passing subject B

The probability of passing subject A is 0.8.

This means that [tex]P(A) = 0.8[/tex]

If you have passed subject A, the probability of passing subject B is 0.8.

This means that [tex]P(B|A) = 0.8[/tex]

Find the probability that the student passes both subjects?

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.8*0.8 = 0.64[/tex]

0.64 = 64% probability that the student passes both subjects.

Find the probability that the student passes at least one of the two subjects

This is:

[tex]p = P(A) + P(B) - P(A \cap B)[/tex]

Considering [tex]P(B) = 0.7[/tex], we have that:

[tex]p = P(A) + P(B) - P(A \cap B) = 0.8 + 0.7 - 0.64 = 0.86[/tex]

0.86 = 86% probability that the student passes at least one of the two subjects

Answer:

3396.65

Step-by-step explanation:

Let's start by cacluating the amount the bank is loaning us

800000*.8=640000

Let's now calculate the effective rate: .049/12= .004083333333

let x= payment

[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]

Answer:

42÷2

Step-by-step explanation:

Answer:

[tex]\frac{28}{n}[/tex]

Step-by-step explanation:

Answer:

Sum = 19,662

Step-by-step explanation:

Given that this is a finite geometric series (meaning it stops at a specific term or in this case -24,576), we can use this formula:  

[tex]\frac{a(1-r^n)}{1-r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.

Substituting for everything and simplifying gives us:

[tex]\frac{6(1-(-4)^7)}{1-(-4)} \\\\\frac{6(16385}{5}\\ \\\frac{98310}{5}\\ \\19662[/tex]

2(x +1) = 16

Use the distributive property ( multiply 2 by each term inside the parenthesis).

2x + 2 = 16

Subtract 2 from both sides:

2x = 14

Divide both sides by 2:

x = 7

Answer:

7

Step-by-step explanation:

2x+2=16

2x=16-2

x=16-2/2

x=14/2=7

Answer:

0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 509 MPa with a standard deviation of 17 MPa.

This means that [tex]\mu = 509, \sigma = 17[/tex]

What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?

This is the p-value of Z when X = 509. So

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

[tex]Z = \frac{509 - 509}{17}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5

0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa

Answer:

15c + 70b < 64,000

Step-by-step explanation:

15c will represent the amount of ounces in the truck from the 15 ounce cans.

70b will represent the amount of ounces in the truck from the 70 ounce bottles.

These need to be added together in the inequality to represent the total weight in the truck.

Then, a less than inequality sign needs to be used, since the truck has to be carrying less than 64,000 ounces.

Put this all together:

15c + 70b < 64,000

So, the inequality is 15c + 70b < 64,000

Answer:

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large shipment of televisions contained 9% defectives

This means that [tex]p = 0.09[/tex]

Sample of size 393

This means that [tex]n = 393[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.

X = 0.12

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812

X = 0.06

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

[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Answer:

The right answer is "[tex]x\simeq 254[/tex]".

Step-by-step explanation:

Let the number of earlier case will be "x".

Now,

⇒ [tex]x+x\times \frac{26.3}{100}=321[/tex]

or,

⇒ [tex]x+x\times 0.263=321[/tex]

By taking "x" common, we get

⇒   [tex]x(1+0.263)=321[/tex]

⇒                    [tex]x=\frac{321}{1.263}[/tex]

⇒                       [tex]=254.15[/tex]

or,

⇒                    [tex]x\simeq 254[/tex]

Answer:

sensory measurement are lower after hypnotism

Step-by-step explanation:

Given the data :

Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6

After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0

The difference ;

After - Before, d = 0.2, - 4.1, - 1.6, - 1.8, - 3.2, - 2, - 2.9, - 9.6

Hypothesis :

H0 : μd = 0

H0 : μ < 0

The test statistic ;

T = μd / sd/√n

Where, xd = mean of difference

sd = standard deviation of difference

n = sample size

Mean of difference, μd = Σx/n = - 3.13

Standard deviation of difference, sd = 2.91

T = - 3.13 / 2.91/√8

T = - 3.13 / 1.0288403

T = - 3.042

α = 0.01

The Pvalue using a Pvalue calculator ;

Degree of freedom, df = n - 1 ; 8-1 = 7

Pvalue(-3.042, 7) = 0.00939

Pvalue < α ; we reject the null and conclude that sensory measurement are lower after hypnotism

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Answer:

  50π cm²

Step-by-step explanation:

The radius of the larger circle is 10 cm, so its area is ...

  A = πr² = π(10 cm)² = 100π cm²

The area of each smaller circle is ...

  A = π(5 cm)² = 25π cm²

Then the shaded area is ...

  shaded = large circle - 2 × small circle

  shaded = 100π cm² - 2(25π cm²) = 50π cm²

Answer:

$10

Step-by-step explanation:

5 toys = $1

Zach wants 50 of these

50 ÷ 5 = 10

10 x 1 = 10

= $10

Answer:

10 dollars

Step-by-step explanation:

We can use a ratio to solve

5 rings     50 rings

----------  = --------------

1 dollar         x dollars

Using cross products

5*x = 1 * 50

5x = 50

Divide by 5

5x/5 = 50/5

x = 10

Answer: The line starts at 1 positive, then from there go -4 (so go to the left) then 1 down from that point.

Step-by-step explanation: the problem is supposed to have been Y= -4/1 +1

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Answer:

  (c)

Step-by-step explanation:

  [tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]

Answer:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]

[tex]P(x < 70) = 0.225[/tex]

Step-by-step explanation:

Given

[tex]Lower = 30[/tex]

[tex]Width = 10[/tex]

Solving (a): The relative frequency table

First, we construct the frequency table using the given parameters.

[tex]\begin{array}{cc}{Class} & {Frequency} &{30-39} & {1} & {40-49} & {1} & {50 - 59} & {2} & {60 - 69} & {5} & {70 - 79} & {13} & {80 - 89} & {10} & {90 - 99} & {8} & {Total} & {40}\ \end{array}[/tex]

The relative frequency (RF) is calculated as:

[tex]RF = \frac{Frequency}{Total}[/tex]

Using the above formula to calculate the relative frequency, the relative frequency table is:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]

Solving (b): [tex]P(x < 70)[/tex]

To do this, we add up the relative frequencies of classes less than 70.

i.e.

[tex]P(x < 70) = [30 - 39] + [40 - 49] + [50 - 59] + [60 - 69][/tex]

So, we have:

[tex]P(x < 70) = 0.025 + 0.025 + 0.050 + 0.125[/tex]

[tex]P(x < 70) = 0.225[/tex]

Answer:

If rounded to the nearest 10 bacteria, then it would be 500 bacteria.

Step-by-step explanation:

First multiply 150 by two in order to get 300, that leaves 4 hours to figure out. From there you can figure out the rest by seeing that 4 is 2/3 of 6. I converted it into the decimal number .66. Multiply 300 by .66 to get 198 and then add it to 300 to get 498. Then just round it up to the nearest 10 bacteria which leaves you with the final answer of 500 bacteria.

Question is incomplete, however here's an explanation to solve questions such as this

Answer and explanation:

Probability= number of favorable outcomes/total number of outcomes

The frequency distribution recorded by the professor would show number of times(frequency) each student missed a class day.

We are required to fund the probability that a student would miss class

Probability = number of times the student missed class/ total number of classes missed by all students

Example, if student missed class 20 times in a semester and all students in total missed class 200 times

Probability that the student would miss class=20/200= 1/10