What is the remainder when 3x2−7x+5 is divided by x+5?

Answer:

We know that the distributive property says this:

a(b+c) = ab + ac

If we apply this to our case, we can put

3a(2b+c) = 3a * 2b + 3a * c

When we multiply numbers and letters, we should multiply both of them:

3a * 2b + 3a * c = 3*2*a*b + 3*a*c = 6ab +3ac

We can use this when we find a number multiplied by a parenthesis..

Answer:

6ab + 3ac

Step-by-step explanation:

3a(2b) + 3a(c)

6ab + 3ac

The number is 90.

Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %. Percentages are a measure of frequency.

When the number is decreased, the number becomes smaller. This means that the original number is larger than 81.

The equation that can be used to represent the information in the question is:

(1 - percentage decrease) initial number = 81

(1 - 0.1)x = 81

0.9x = 81

x = 81 / 0.9

x = 90

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Answer:

Correct Answer: 512

Step-by-step explanation:

\(8^7\) · \(8^{-4}\) · \(4^0\)

Multiply \(8^7\) by \(8^-4\) by adding the exponents.

Use the power rule \(a^m a^n=a^{m+n}\)  to combine exponents.

\(8^{7-4}\) · \(4^0\)

subtract 4 from 7

\(8^{3}\) ·  \(4^0\)

Simplify \(8^{3}\) ·  \(4^0\) ←

\(8^{3}\) · 1 ←

Raise  8  to the power of   3

512

Sabastien didn't simplify correctly, he Raised 4 to the power of 0 and turned the 1 into 0. which was incorrect. where the outcome should've been 1.

It would take 21 8/ 12 seconds to fill 2 tires

Proportion can be defined as the comparison between two numbers or elements

It is also an equation with two ratios draw equal to each other.

From the information given,

If 31/ 3 tires (10/ 3 ) tires is filled in 3 1/4 seconds ( 13/ 4)

Then 2 tires = x seconds

cross multiply

x = 13 / 4 × 2 ÷ 10/ 3

x = 26/ 4 × 3/ 10

x = 260/ 12

x = 21 8/ 12 seconds

Thus, it would take 21 8/ 12 seconds to fill

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The consequence of violating the assumption of Sphericity can be significant. It reduces statistical power, effects the distribution of the F-statistic, and raises the rate of Type I errors in post hocs.

Sphericity refers to the homogeneity of variances between all possible pairs of groups in a repeated-measures design. When this assumption is violated, it can result in a distorted F-statistic, which in turn affects the results of post hoc tests.
The correct answer to the question is c. It reduces statistical power, effects the distribution of the F-statistic, and raises the rate of Type I errors in post hocs. This means that violating the assumption of Sphericity leads to a decreased ability to detect true effects, an inaccurate representation of the true distribution of the F-statistic, and an increased likelihood of falsely identifying significant results.
According to statistics, the consequence of violating the assumption of Sphericity is not a rare occurrence. Therefore, it is essential to ensure that the assumptions of your statistical analysis are met before interpreting your results to avoid false conclusions.
In conclusion, violating the assumption of Sphericity can have severe consequences that affect the validity of your research results. Therefore, it is crucial to understand this assumption and check for its violation to ensure the accuracy and reliability of your statistical analysis.

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The value of x is 13.

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

We have,

Two lines m and n are parallel.

Two angles (7x -1)° and (8x - 14)° are corresponding angles.

We know that corresponding angles are equal.

We can write as:

7x - 1 = 8x - 14

We will find the value of x.

We will keep the like terms on one side.

14 - 1 = 8x - 7x

13 = x

x = 13

Therefore the value of x is 13.

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Answer:

Here

Step-by-step explanation:

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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By referring to the table that summarizes service times of dinners at a fast food restaurant, we can see that there are 49 individuals who are included in the summary.

We may calculate the total number of people by simply adding the frequencies:

9 + 20 + 13 + 4 + 3 = 49 people

A measure of an event's frequency is how often it occurs within a specific time frame. For clarity, it is sometimes referred to as temporal frequency and is distinct from angular frequency. The class interval is the distance between the top and lower class bounds of a frequency distribution table. Data are discrete pieces of factual information that are logged and used for analysis. Raw data is the foundation from which statistics are derived. Statistics are the results of data analysis, including its interpretation and presentation. The outcomes of data analysis, including its interpretation and presentation, are statistics. It includes techniques for data collection, evaluation, analysis, and interpretation, is the study and manipulation of data.

Note that the full question is:

Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?

Time (sec) Frequency

60 to 119 9

120 to 179 20

180 to 239 13

240 to 299 3

300 to 359 4

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Answer:

there's one solution bc the lines have one point in common

Answer:

\( \sin(R) = \frac{6}{ \sqrt{97} } \)

Step-by-step explanation:

Sin R = Opposite / hypotenuse

I hope I helped you^_^

To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

Samantha is 21

Step-by-step explanation:

103/5=20.6 round down to 20 and since they are consecutive integers, 21.

Answer:

Step-by-step explanation:

The x-coordinate of the vertex is determined by:

So we have:

Now, substitute x- and y- values to find the value of c:

Answer:

-14x + 6

Step-by-step explanation:

-12x + 6 - 2x

-14x + 6

The two processes that caused the puddle to form and then disappear were evaporation and infiltration.

Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.

Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.

The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.

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Answer:

Step-by-step explanation:

credits to numerade

area of ∆PQR/ area of ∆WUV = 1/9

Step-by-step explanation:

Part A

A) The denominator is 665, so this is a terminating decimal.

B) 11/99 = 1/9 = 0.1111...

C) 256/999 = 0.256256256...

D) 25/909 = 275/9999 = 0.027502750275...

B has 1 repeating digit, C has 3 repeating digits, and D has 4 repeating digits.  So the correct answer is C.

Part B

A decimal that can be written as a ratio of integers is a rational number.

Answer:

blahaha

Step-by-step explanation:

hahaha

The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).

We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.

E = x³ - 6x² + 3x + 10

One of the factors in the expression is already given. The given factor is (x + 1).

Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.

E = (x + 1)(x² - 7x + 10)

Now we will factorise the quadratic expression.

E = (x + 1)[x² - 2x - 5x + 10]

E = (x + 1)[x(x - 2) - 5(x - 2)]

E = (x + 1)(x - 2)(x - 5)

We cannot simplify and factorise the expression any further.

Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).

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a) The Probability density function of given uniform distribution example is

F(x) = 1/3.5 for 8.5 < x< 12

Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where

x ---> minimum value and y---> maximum value

Probability density function is a probability function which defines the density of continuous random variable lying between specified range

values. It is denoted by f( a<X<b)

Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.

We have following informations,

weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.

Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.

this implies a = 8.5 , b = 12

F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12

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#Complete Qestion :

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?

The area of this hub cap is about 470.46 square centimeters.

To calculate the circumference of the the formula is given below is used.

Circumference (C) = 2π radius

Replacing with the values given:

76.87 = 2 (3.14) r

Solving for r (radius)

76.87/ (2x 3.14) =r

r = 12.24 cm

To find the Area:

Area of a circle = π r²

A = 3.14 (12.24)^2

A = 470.46 cm²

If the circumference of the hub is smaller, the area is also smaller because it means that the radius of the circle decreases.

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Answer:

x = -4

Step-by-step explanation:

\( - 3x = 12\)

Lets divide both the sides by -3.

\( = > \frac{ - 3x}{ - 3} = \frac{12}{ - 3} \)

\( = > x = - 4\)

x= -4

-3x=12

divide x by -3 and do the same on the other side

12÷(-3)= -4

hence, x= -4

if you want to check if something is right, substitute your answer into the question

hope this helped

Distance from Y to Z is 10.4 km and Z to X is 20 km

Distance is a numerical measurement of how far apart objects or points are.

A triangle is a polygon with three edges and three vertices.

From the given data plot the graph,

Then,

∠XYZ=∠YZX=75 degrees

Therefore XY=XZ=20 km

\(YZ^{2}=20^{2} +20^{2} -2(20)(20)cos30\)

YZ=10.4 km

Hence, Distance from Y to Z is 10.4 km and Z to X is 20 km

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Answer:

Step-by-step explanation:

The third side cannot be 1.

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side.

Given:

Two sides are 2 and 3.

As, we know that the third side of triangle is greater than sum of other two side of triangle.

So, 2+ 3 = 5

So, 1+ 2 > 3

and, 2+ 2 >3

and, 3+ 2 >3

Hence, the third side cannot be 1.

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Answer:

-16

Step-by-step explanation:

d - 8 / -2 = 12

d - 8 = 12 * -2

d - 8 = -24

d = -24 + 8

d = -16

Answer:

The volume of a sphere is given by the formula:

V = (4/3)πr³

where r is the radius.

Substituting the given value of r=81cm, we get:

V = (4/3)π(81)³

V = (4/3)π(531441)

V = 904779.5π

Therefore, the volume of the sphere is approximately 2,847,892.22 cubic centimeters (rounded to two decimal places).

Volume of the sphere is 708588π cm³ when the radius of a sphere is 81 cm and formula is \(\frac{4}{3} \pi r^3\).

Given that,

The radius of a sphere is 81 cm.

We have to find what is the volume of the sphere.

We know that,

The amount of area occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its center, creating a three-dimensional round solid object.

The formula for the volume of the sphere is \(\frac{4}{3} \pi r^3\).

So,

r is the radius of the sphere is 81 cm.

We get,

Volume of the sphere = \(\frac{4}{3} \pi (81)^3\)

Volume of the sphere = 4×π×27×81×81

Volume of the sphere = 708588π cm³

Therefore, Volume of the sphere is 708588π cm³.

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Juan has more savings than Fawzia is t > 4.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: Juan had $50 in savings and saved an additional $20 each week thereafter. Fawzia started the year with $90 and saved $10 every week.

Juan

Saving = $50

Additional = $20

So, the function is

J(t) = 50 + 20t

Fawzia

Saving = $90

Additional = $10

So, the function is

F(t) = 90 + 10t

Next, we plot the graphs of J(t) and F(t)

From the graph, the interval of time when Juan has more in savings than Fawzia is t > 4

Hence, Juan has more savings than Fawzia is t > 4.

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