Use distributive property to complete the equivalent expression. Enter your answer in the boxes. 4(y - 3) =

Answer:

\(45*(9x^2+4)\)

Step-by-step explanation:

STEP

1

:

Equation at the end of step

1

:

((5x2•(34))+(5•(33)))+(5•32)

STEP

2

:

Equation at the end of step 2

((5x2•(34))+(5•(33)))+(5•32)

STEP

3

:

Equation at the end of step

3

:

((5x2 • (34)) + (5 • 33)) + (5•32)

STEP

4

:

Equation at the end of step 4

((5x2 • (34)) + (5•33)) + (5•32)

STEP

5

:

Equation at the end of step

5

:

((5x2 • 34) + (5•33)) + (5•32)

STEP

6

:

Equation at the end of step 6

((5•34x2) + (5•33)) + (5•32)

STEP

7

:

STEP

8

:

Pulling out like terms

8.1 Pull out like factors :

405x2 + 180 = 45 • (9x2 + 4)

Polynomial Roots Calculator :

8.2 Find roots (zeroes) of : F(x) = 9x2 + 4

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 9 and the Trailing Constant is 4.

The factor(s) are:

of the Leading Coefficient : 1,3 ,9

of the Trailing Constant : 1 ,2 ,4

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 13.00

-1 3 -0.33 5.00

-1 9 -0.11 4.11

-2 1 -2.00 40.00

-2 3 -0.67 8.00

Note - For tidiness, printing of 13 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

45 • (9x2 + 4)

Based on the scatterplot, the form of the relationshipbetween fire spread rate and wind speed   can be described as a positive correlation.

As wind speed increases,the fire spread rate also tends   to increase.

b. Direction  -

Based on the given scatterplot,the direction of the relationship between fire spread rate and wind speed appears to   be positive.

As the wind speed   increases,the fire spread rate generally tends to increase as well.

c. Strength  -

The scatterplot suggests a   moderate to strong relationship between fire spread rate and wind speed.

The data points   exhibit a somewhat linear pattern, indicating that there is a noticeable association between these variables.

The firespread rate tends to increase consistently as the wind speed increases, suggesting a relatively strong positive correlation between the two factors.

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Full Question:

Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents.

Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.

Wind Speed (miles/hour) Fire Spread Rate (feet/minute)

0.76                                         0

1.78                                             2

3.34                                                4

5.38                                       6

8.10                                                8

11.75                                     10

16.70                                    12

A scatterplot of these data is shown here  -

1. Based on the scatterplot, how would you describe the following with regard to the relationship between fire spread rate and wind speed?

a. Form:

b. Direction:

c. Strength:

Answer:

which one substitution or elimination

Step-by-step explanation:

Substitution: (-1,-3 )

Elimination: (-1,-3)

i hope this helps you :)

Please mark me brainlest

Tan(48.9) = x/138

X = 138 x tan(48.9)

X = 158.2

SOLUTION:

Case: Euler's formula

Given:

Faces= 20

Vertices =12

Euler's formula: F + V = E + 2

Required: To find the number of Edges

Method:

Step 1: Recreate the formula to isolate E

F + V = E + 2

E = F+V - 2

Step 2: Plug in the value of the variables

E = F+V - 2

E= 20 + 12 - 2

E = 30

Step 3:

The value of E is 30

Final answer:

The Polyhedron has 30 edges

Answer:

74 inches

Step-by-step explanation:

87

Answer:

I can see ur question but I'm not getting it is there any answers I can chose from to work it out

Answer:

Both triangles are similar by SAS

Step-by-step explanation:

See attachment for triangles

\(\triangle OKJ\) and \(\triangle ONM\)

From the attachment:

\(OK = 3; OJ = 30; KN = 1; JM = 3\)

Calculate the lengths of ON and OM

\(ON=OK+KN=3+1= 4\)

\(OM = OJ + JM = 30 + 10 = 40\)

To determine if both triangles are similar or not, we make use of the following equivalent ratios

\(OK : OJ = ON : OM\)

\(3 : 30 = 4 : 40\)

Divide the first ratio by 3 and the second by 4

\(1:10 = 1 : 10\) --- This implies that both triangles have 2 similar sides

From the attachment,

\(\angle KOJ = \angle NOM\) ---- similar angles

Since the two triangles have 2 similar sides and a similar angle, then both triangles are similar by SAS

Answer:

(4/x) - 1 is the way to represent this equation.

Answer:

P.ut your age since you're the bus driver

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.

Answer:

Step-by-step explanation:

A. 60 + 30 = 90

B. 690000

C. 90 x 2000 = 180000

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

\(\tan D=\frac{7}{4},\\\\\sin D=\frac{7}{8.1}, \\\\\cos D=\frac{4}{8.1}, \\\\GI=5.0\)

Step-by-step explanation:

In any right triangle, the following is true:

The sine of any angle is equal to its opposite side divided by the hypotenuse of the triangle. (o/h)

The cosines of any angle is equal to its adjacent side divided by the hypotenuse. (a/h)

The tangent of any angle is equal to its opposite side divided by its adjacent side. (o/a)

Thus,

\(\text{3. }\\\tan D=\frac{7}{4},\\\\\sin D=\frac{7}{8.1}, \\\\\cos D=\frac{4}{8.1},\)

\(\text{4. }\tan 68^{\circ}=\frac{GI}{2},\\GI=2\tan68^{\circ}=4.95017370683\approx \boxed{5.0}\)

Hey there! I'm happy to help!

When you divide fractions, you are technically multiplying by the reciprocal, which is the numerator and denominator flipped. This means that 22/33 divided by 6/9 is equal to 22/33 multiplied by 9/6.

If we multiply these together, we get an answer of 1.

I hope that this helps! Have a wonderful day!

The calculated division of the numbers 22/33 divided by 6/9 is 1

From the question, we have the following parameters that can be used in our computation:

22/33 divided by 6/9

When represented as an equation, we have

22/33 divided by 6/9 = 22/33 ÷ 6/9

Represent as a product expression

So, we have

22/33 divided by 6/9 = 22/33 * 9/6

So, we have the following result

22/33 divided by 6/9 = 1

Using the above as a guide, we have the following:

the result is 1

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None of the chosen pairs will be dependent as nothing is specified.

Independent events are those events whose occurrence does not have any effect on the events that may occur or occurred.

Dependent events are those vents whose occurrence either depends on some other event or has an effect on occurring or occurred vents.

Given, The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.

As not mentioned that what kind of book he chooses first or types of book.

Also which shelf he chooses first choosing the first book is independent

and choosing the second book is also independent so none of the chosen pair will be dependent.

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Answer:

64,000

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

12345

If you try to write other numbers like 678910, it will be six digits

9514 1404 393

Answer:

  A

Step-by-step explanation:

Vertical multiplication of polynomials is virtually identical to vertical multiplication of integers. The "place value" associated with a column is the power of the variable. When adding within a column, there is no "carry" to the next column the way there is with integers.

Here, the correct answer choice can be found by looking at the coefficients of x^2 and of x.

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of how to calculate the p-value for the hypothesis test:

Step 1: State the null and alternative hypotheses

The null hypothesis is that the true population mean weight of stoaches is 308 g, and the alternative hypothesis is that the true population mean weight is not 308 g.

H0: µ = 308 g (null hypothesis)

Ha: µ ≠ 308 g (alternative hypothesis)

Step 2: Determine the test statistic

We can use a t-test to determine the test statistic for this hypothesis test. The test statistic is given by:

t = (sample mean - hypothesized mean) / (standard error of the mean)

where the sample mean is 313.8 g, the hypothesized mean is 308 g, and the standard error of the mean is calculated as:

standard error of the mean = standard deviation / sqrt(sample size)

Substituting the given values, we get:

t = (313.8 - 308) / (58 / sqrt(54))

t = 1.547

Step 3: Determine the p-value

To determine the p-value, we need to find the probability of obtaining a test statistic as extreme or more extreme than our observed t-value, assuming the null hypothesis is true. Since we have a two-sided alternative hypothesis, we need to find the area in both tails of the t-distribution that is more extreme than our observed t-value.

Using a t-distribution table or calculator with 53 degrees of freedom (since we have a sample size of 54), we find that the probability of obtaining a t-value of 1.547 or greater is 0.0722 in the right tail, and the probability of obtaining a t-value of -1.547 or less is also 0.0722 in the left tail. Therefore, the p-value for the two-sided test is the sum of these two probabilities:

p-value = 0.0722 + 0.0722

p-value = 0.1444

Step 4: Compare the p-value to the significance level

The significance level is typically set to 0.05 for hypothesis tests. Since our calculated p-value (0.1444) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to suggest that the true population mean weight of stoaches is different from 308 g.

In summary, the p-value for the two-sided hypothesis test is 0.1444, and since this value is greater than the significance level of 0.05, we do not reject the null hypothesis.

Answer:

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

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 \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

If \(|Z| > 2\), the value of X is considered to be unusual.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.

This means that \(\mu = 100, \sigma = 15\)

Sample of 3

This means that \(n = 3, s = \frac{15}{\sqrt{3}}\)

Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

We have to find the z-score.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}\)

\(Z = 1.73\)

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Answer:

\(\huge\boxed{\sf x =5 \ \ \ OR \ \ \ x = 1}\)

Step-by-step explanation:

\(x^2-6x+5=0\)

\(x^2-5x-x+5=0\\\\Take \ common\\\\x(x-5)-1(x-5)=0\\\\Take \ (x-5) \ common\\\\(x-5)(x-1)=0\)

Either,

x - 5 = 0         OR         x - 1 = 0

\(\rule[225]{225}{2}\)

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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Answer:

f(6)=-42

f(0)=0

f(-1)=7

Step-by-step explanation:

since f(x) =-7x

it implies that f(6),f(0) and f(-1) are all equal to f(x)

which is equal to -7x .

so wherever you find x you out it in the

function

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

The graph of the line segment after the translation (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5) has been drawn.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given coordinate,T(1,2) and U(4,6)

Apply the translation (x, y) → (x-2, y-3)

T(1,2) → T'(1 - 2,2 - 3) = T'(-1,-1)

U(4,6) →  U'(4 - 2,6 - 3) = U'(2,3).

Apply the translation (x, y) → (x-4, y + 5)

T(1,2) → T'(1 - 4,2 + 5) = T'(-3,7)

U(4,6) →  U'(4 - 4,6 + 5) = U'(0,11)

All points have been plotted below.

Hence"After the translations (x, y) → (x-2, y-3)  and (x, y) → (x-4, y + 5), the graph of the line segment has been drawn.".

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Answer:

Translation (x, y) → (x - 2, y - 3):

Translation (x, y) → (x - 4, y + 5):

Step-by-step explanation:

Given endpoints of line segment TU:

Translation 1 (blue on attached diagram)

This means to subtract 2 from the x-values of the endpoints, and subtract 3 from the y-values of the endpoints:

Therefore:

Translation 2 (red on attached diagram)

This means to subtract 4 from the x-values of the endpoints, and add 5 to the y-values of the endpoints:

Therefore:

Step-by-step explanation:

Given

f(x) = 2x - 4

Then

f(2) = 2 * 2 - 4

= 4 - 4

= 0

Therefore f(2) = 0 .

Hope this helps :)

The value of n(AUB) i.e. union of A and B is 53.

What are Intersections and Unions in Probablity?

The union of two sets results in a new set that contains all of the items from both sets. The union is abbreviated as A∪B or "A or B." The intersection of two sets yields a new set containing all of the members from both sets. The junction is denoted by the letters A∩B or "A and B."

Solution:

Given that,

n(A) = 14

n(B) = 51

n(A∩B) = 12

We know that thee formula is n(AUB) = n(A) + n(B) - n(A∩B)

Putting the values,

n(AUB) = 14 + 51 - 12 = 53

So, the answer for the value of n(AUB) = 53

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The probability that both events happen is given as follows:

P(A and B) = 1/3.

The probability of event B is given as follows:

P(B) = 1/2.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A dice has six sides, which are given as follows:

1, 2, 3, 4, 5 and 6.

Hence the probabilities for each event are given as follows:

The events are independent, hence the probability of both events is given by the multiplication of the probabilities of each event, as follows:

2/3 x 1/2 = 1/3.

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