Write a possible polynomial function in factored form with roots 0, - 5 , and3

Answer:

The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.

Step-by-step explanation:

Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.

At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So

\(H_0: \mu = 350\)

At the alternate hypothesis, we test if this mean increased, that is:

\(H_1: \mu > 350\)

The test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

350 is tested at the null hypothesis:

This means that \(\mu = 350\)

After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.

This means that \(n = 35, X = 405, s = 25\).

Test statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}\)

\(t = 13.02\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.

Using a t-distribution calculator, this probability is of 0.

The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.

Based on the length of BC and AC, we can find the length of AB to be 112cm.

This is a right-angled triangle which means that we can use the Pythogorean theorem to solve for the length of AB which is the hypotenuse.

The length of AB is:

AB² = BC² + AC²

Solving gives:

AB² = 63² + 93²

AB² = 3,969 + 8,649

AB = √(12,618)

AB = 112 cm

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The magnitude of the resultant of two vectors must be greater than or equal to the magnitude of each of these vectors. - False

The magnitude of the vector product formed by two other vectors need not be bigger than or equal to the magnitude of the original vectors. The vector produced when two vectors are added together is known as the resultant. The Pythagorean theorem, which asserts that the square of the magnitude of the resultant is equal to the sum of the squares of the magnitudes of the two vectors, is used to determine the magnitude of the resultant.

According to the angles formed by the two vectors, the magnitude of the results may be larger than, equal to, or less than the magnitudes of the two vectors. The magnitude of resultant will equal the total of magnitudes of two vectors if the vectors are at right angles to one another. The magnitude of resultant will be less than total of the magnitudes of the two vectors if the vectors are not at right angles to one another.

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Answer:

$2376

Step-by-step explanation:

Money Marc withholds from his gross income in taxes and deductions: We can do this by multiplying his gross income by the withholding rate of 28%, which gives us 0.28 * $3,300 = $<<0.28*3300=924>>924.

Next, we need to subtract this amount from Marc's gross income to find his net pay. This gives us $3,300 - $924 = $<<3300-924=2376>>2376. Therefore, Marc's monthly net pay is $2376.

Answer:

ii. \((a^{2} +b^{2} +2bc+c^{2} )(a+b+c)(a-b-c)\)

v. \((x^{2} -y^{2} )^{2}\)

Step-by-step explanation:

ii. \(a^{4} -(b+c)^{4}\)

\(=(a^{2} )^{2} -((b+c)^{2} )^{2}\) (Rewrite using Exponent Rules)

\(=(a^{2} +(b+c)^{2} )(a^{2} -(b+c)^{2} )\) (Difference of Squares)

\(=(a^{2} +b^{2} +2bc+c^{2} )(a+(b+c))(a-(b+c))\) (Expand the terms in the first parentheses, use the difference of squares again to further factor the terms in the second parentheses)

\(=(a^{2} +b^{2} +2bc+c^{2} )(a+b+c)(a-b-c)\) (Simplify)

v. \(x^{4} -2x^{2} y^{2} +y^{4}\)

\(=(x^{2})^{2} -2x^{2} y^{2} +(y^{2} )^{2}\) (Rewrite using Exponent Rules, notice that this is now a perfect square trinomial)

\(=(x^{2} -y^{2} )^{2}\) (Factor using perfect square trinomial formula)

Hope this helps!

Answer: b. x>5

Step-by-step explanation:

Answer:

  14

Step-by-step explanation:

Look for 10 in the f(x) column. This is the output value.

Find the corresponding value in the x-column. This is the input for that output value.

The input that corresponds to an output of 10 is x=14.

The value of the invoice on May 18 is $3200.

Amount of invoice on May 17 = $4000

Percentage decrease = 20%

Decrease in amount = 20% × $4000 = 0.2 × $4000 = $800

Therefore, the value of the invoice on May 18 will be:

= Amount of invoice on May 17 - Reduction in the amount

= $4000 - $800

= $3200

Therefore, the value of the invoice on May 18 is $3200

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IT MEANS THAT THE X COORDINATE CHANGED BY -4

\(x = 6 - 4 \\ x = 2\)

THE NEW COORDINATE OF X IS 2

AND THE Y COORDINATE CHANGED BY +7

\(y = - 2 + 7 \\ y = 5\)

THE NEW COORDINATE OF Y IS 5

(2,5)

ATTACHED IS THE SOLUTION

9x^2+9x+2

The trinomial is in the form:

ax^2+bx+c

Where:

a=9

b= 9

c=2

First, multiply a by c:

9 x 2 = 18

then, find product that equal 18

2 x 9 = 18

1 x 18 = 18

6 x3 =18

Find the the one that added equal to b-

b= 9

6+3 = 9

Rewrite the trinomial with new numbers added in the middle term place:

9x = 6x+3x

9x^2+6x+3x+2

Isolate similar terms and factor by Great Common factor:

(9x^2+3x) +(6x+2)

3x (3x+1)+2(3x+1)

Factor out 3x+1

(3x+2) (3x+1)

The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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The system of equations we need to solve is:

x*90 + y*50 = 860

y = x + 6

Solving that we will see that there are 4 mini hot dogs and 10 pizza rolls.

First, we need to define the variables we will be using, these are:

x = number of mini hotdogs.

y = number of pizza rolls.

We know that the combination has 860 calories in total, so:

x*90 + y*50 = 860

We also know that there are 6 more pizza rolls than mini hotdogs, so:

y = x + 6

Then the system of equations is:

x*90 + y*50 = 860

y = x + 6

Replacing the second equation into the first one, we will get:

x*90 + (x + 6)*50 = 860

Now we can solve this for x.

x*90 + x*50 + 300 = 860

x*140 + 300 = 860

x*140 = 860 - 300

x*140 =  560

x = 560/140 = 4

So there are 4 mini hotdogs, and:

y = x + 6

y = 4 + 6 = 10

There are 10 pizza rolls.

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Ryan's error lies in not utilizing the right units for measurement. He used inadequate milk and wrong flour measurement, influencing the recipe's proportion and result.

Ryan's error lies in not utilizing the right units for measurement. The formula calls for 0.25 quart of drain and 2.5 glasses of flour. Ryan utilized 1/5 quart of drain (which is less than 0.25 quart), and rather than utilizing glasses for flour, he utilized 9/4 mugs (which is identical to 2.25 mugs, not 2.5 glasses).

This bungle of units and wrong measurements might lead to the rolls having the off-base consistency and taste due to the awkwardness of fixings. It's imperative to use the desired units and estimations in formulas to realize the expected result.

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Answer:

c. 2

Step-by-step explanation:

the Y- intercept is 2 because it says +2

The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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The future value of the investment is equals to $\(32,582.78\).

The number of monthly payments over 4 years is:

= 4 years x 12 months/year

= 48 months.

We will use future value of an annuity formulae to solve which is FV = PMT x [(1 + r)^n - 1] / r

Plugging in the values, we get:

FV = 650 * [(1 + 0.022/12)^48 - 1] / (0.022/12)

FV = 650 * (0.09190014604/0.00183333333)

FV = 650 * 50.1273524766

FV = 32582.7791098

FV = $32,582.78.

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Answer:

B. Multiply the divisor and dividend by 100.

Step-by-step explanation:

Multiply by 100 to get rid of the decimal

Answer:

B. Multiply the divisor and the dividend by 100

Step-by-step explanation:

i did the question on a test

Answer:

x15 y90 z13

Step-by-step explanation:

https://dlsfile.com/dd/MTQ1ODE5a3Bjd2hiaGxmXzM0MTMyNQ

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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0

Because the line isn't increasing or decreasing, it's just flat, so it's 0.

Answer:

Step-by-step explanation:

It doesn't matter what value x has. y is always 2. That means that the slope has disappeared.

The slope must be zero.

Answer:

There is no solution.

Answer:

12

Step-by-step explanation:

Answer:

y = -3x/4 + 4

Step-by-step explanation:

slope m = -3/4

-2=(-3/4)×8+b

or, b = 4

y = mx + b

y = -3x/4 + 4

Answered by GAUTHMATH

The 3/8 chance is the probability of winning a scholarship.

The odds of winning a scholarship is 3/5

The probability is given as:

P(Win) = 3/8

The odds is calculated using:

Odds = P(Win)/[1 - P(Win)]

This gives

Odds = 3/8/[1 - 3/8]

Evaluate the difference

Odds = (3/8)/(5/8)

Evaluate the quotient

Odds = 3/5

Hence, the odds of winning a scholarship is 3/5

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Letter A doesn't show rotational symmetry of 180 degrees.

The letter 'A' has just one vertical line of symmetry.A vertical line of symmetry is that line which runs down a picture thus dividing it into two identical halves. In other words, it's a straight standing line that divides an image or shape into two identical halves.

The rotational symmetry of a shape explains that when an object is rotated on its own axis, the form of the object looks the same. Many geometrical shapes appear to be symmetrical once they are rotated 180 degrees or with some angles, clockwise or anticlockwise. A number of the examples are square, circle, hexagon, etc.

Complete Question-  A rotation of 180 degrees maps figure A onto itself. It has transformation or not?

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Answer:

No

Step-by-step explanation:

If these two individual statements are true, it means they share the same elements of set C. In addition to this, sets A and B could have additional elements, hence this cannot be true.

Answer: 25%.

Step-by-step explanation:

According to the problem it states that the original price is 48 dollars which is 100% cost. We know that 12 is 1/4 of 48 so 1/4 of 100% gives 25%.

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)