can it be concluded at a 0.01 level of significance that there is a linear correlation between the two variables?

93 is more than 47 by 46

Subtraction is an arithmetic operation that represents the operation of removing a number from another number. Subtraction is represented by the minus sign,

Other arithemetic operations are addition, multiplication and division.

The mathemetical properties that it follows is Identity Property.

Commutative Property and Associative Property.

Let the number by how much 47 is less than 93 be x,

then

47 + x = 93

x = 93 - 47

x = 46

Therefore, By subtracting it is found that 93 is greater than 47 by 46

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Refer to the attachment for graph:

What is rotation ?

The rotation of a point with regard to the origin is described by the rotation formula. To get the position of the point after rotation, apply the rotation formula. Rotation is a circular movement about the specific axis or point of rotation. In general, there are two common directions for rotation: clockwise and anti-clockwise or counter-clockwise.

An object moving in a circle around its center is said to as rotating. Rotation can occur in a variety of ways. Earth's rotative motion

During 180° rotation about origin,

the x and y coordinates changes to their negative values.

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The null hypothesis for the no difference test is 0 and the alternative hypothesis is 4.905 using the level of significance.

a)null hypothesis (H₀) = 0

Alternative hypothesis (H₀) ≠ 0

t = (d)/√n = 850 × √42 ÷ 1123 = 4.902

b) Now we calculate the degrees of freedom given by:

degrees of freedomf

= n-1

= 42 -1

= 41

Now we can calculate the p value, we have a left tailed test the p value is given by:

p=2× P(t₍₄₁₎>4.905) = 0.00015

We can therefore infer that we can reject the null hypothesis that the difference between the two groups is equal because the p value is less than the significance level indicated.

When there are two samples and the data in one sample can really be paired with observations in the other sample, a paired t-test is used to compare the two population means.

The system of the null and alternate hypothesis for this particular case are:

Null hypothesis: μ₁ - μ₂ = 0

Alternative hypothesis:  μ₁ - μ₂ ≠ 0

Or equivalently

Null hypothesis: (H₀) = 0

Alternative hypothesis: (H₀) ≠ 0

c) now it is calculated that  μ₁ - μ₂ = 0 , hence we can conclude that The standard deviation for the mean for groceries is more than the mean for dining out .

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The divisor is referred to as a dividend factor if it totally divides the payout, leaving no residual.

A divisor in a calculation is a number that divides the other number. According to the definition of a divisor, it is the term used to divide a dividend. For any division procedure, the remainder is always less than the divisor. All integers can be divided by 1, which is. The divisor will always equal one if the quotient and dividend are equal. The quotient will always equal one if the dividend and the divisor are equal. If there is no residue, the number can be divided evenly and is hence a perfect divisor of the dividend. The quotient will always equal a decimal number if the divisor is greater than the dividend.

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Answer:

32 black grapes

Step-by-step explanation:

24 green grapes

3:4

24÷3=8

8×4=32

there are 32 grapes

Null hypothesis assumes that there is no relationship between the two variables( dependent and independent ).

As given in the question,

Following hypothesis assumes that there is no relationship between variables.

a. Alternate hypothesis: There is a relation between two variables.

b. Null hypothesis : There is no relation between two dependent and independent variables.

c. Secondary : It depends on the primary hypothesis.

d. Research : It is study of systematic inquiry after colleting data.

e. Substantive : research based on particular subject.

Therefore, null hypothesis assumes there is no relation between two variables.

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Answer:

fishing + camping = 15

not fishing + camping = 10

The probability that the student is satisfied with the tentbook is given by 56% or 0.56

Given that,

Let A denotes the event that student used book by Professor A

Similarly B and C

let X be the event that student is satisfied

P [ Student is satisfied given he used a book by professor A ]=

= P[x / A ] = 200/500

= 0.4

Also

P[X/B] = 150/300 = 0.5

P [X/C] = 160/200 = 0.8

Also P(A ) = P(B ) = P(e) = 1/3

The probability that the student is satisfied with the textbook is givenby

P( x ) = P(A). P (x / A ) + P(B ). P( X/B ) + P(e ) P(x/e )

=1/3(0.4) + 1/3(0.5) + 1/3(0.8)

= 0.56667

Hence, The probability that the student is satisfied with the textbook is given by 56%

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Given:

Length of neighbourhood park = 115 inches

Length of actual park = 138 yards

Since 1 yard = 36 inch

Therefore , 138 yards = 138 × 36

                                     = 4698 inches

The price of the widgets for which it should be sold to make the maximum profit is $25.4   .

We know that the quadratic equation ax² + bx + c ,

if a < 0 , then the maximum value of the quadratic equation will be at x = -b/2a .

In the question ,

it is given that ,

a company is selling a widget ,

the selling price of each widget is = x ,

the profit made by the company = y ,

the equation of profit is given as y = −3x² + 152x − 1150 ,

where a = -3 , b = 152 and c = -1150,

we can see that in the given quadratic equation ,

a < 0 , so , the maximum will be at

x = -b/2a

x = -152/2(-3)

x = 152/6

x = 25.333

x ≈ 25.4

Therefore , the price of the widget is $25.4  .

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Answer: the answer is 1.2%

We have to calculate the  minimum distance between the ships by using pythagoras theorem

Let us assume that we have to find the distance at 4 pm from the noon so,

Distance traveled by A in 4 hours  = 15 X 4 = 60mi...........(a)

Distance traveled by B in 4 hours  = 12 X 4 = 48...........(b)

Total distance between A and the initial point of B is = 40 + 60

=100 mi

[tex]c = \sqrt{100^{2} +48^{2}[/tex]

from pythagoras theorem we have,

[tex]a^{2} + b^{2} =c^{2}[/tex]

= [tex](a + 40)^{2} + b^{2} = c^{2}[/tex]

Diff, with respect to time we get the equation ,

[tex]2(a +40)da/dt + 2bdb/dt = 2c dc/dt\\(a+40)da/dt + db/dt = dc/dt\\dc/dt = (a+40)da/dt + b db/dt / c\\dc/dt = (60+40) X 15 + 48 X 12 / \sqrt60^{2}+48^{2} \\dc/dt = 2976 \//\sqrt{2304 +3600}\\dc/dt = 2976/ 76.83\\=38.73[/tex]{ after using equation (a) & (b) }

So, the distance between the ship at 4 pm is changing at 38.73 mph

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The product of two numbers is negative. Which statement is true

B and E

How does the law of signs for multiplication work?

For division and multiplication: Positive results are obtained if the symptoms are same. If the signs disagree, the outcome is adverse.

Detailed explanation:

Let a and b be two separate numbers. A and B together have a negative product. The reason why the product of a and b is negative, according to the law of signs for multiplication, is because a and b have distinct signs—one is positive and the other is negative.

which claim is accurate?

A. The two numbers' quotient is a positive number. NO.

B. The two numbers' quotient is negative. YES. The quotient of two numbers with different signs is negative in accordance with the law of signs for division.

C. The quotient cannot be used to infer any conclusions. NO.

D. Both numbers have negative signs. NO.

E. One number has a positive sign, whereas the other has a negative sign. YES.

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a)The expected number of ER admissions per week is 800.

b)The probability they will make 800 or more ER admissions during a typical week is 1.

We have given that on average the number of admission on weekdays is 100

So, in five days number of admission are =5×100=500

Now, in weekend we have given that 150 admissions comes per day

So, in two days number of admission are =2×150=300

So, Total number of admissions =500+300=800 admissions.

b)We can see that total number of admissions are 800 on average, so it is the average number of admissions.

Here, we can see that this is the event of 100% occurrence. There are no chances of failure.

So, maximum probability of getting 800 or more ER admissions is 1.

Hence, a)ER admissions are 800 b)The probability of 800 or more admission is 1.

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The variance of 1 means that the values of the given data set are relatively more than the expectations.

According to the question,

We have the following information:

Variance of 1

Now, we know that the variance of 1 means that the values in the data set are relatively more than our expectations.

Now, we also know that if the the variance for a given data set is less than 1 then it can be considered that the variance is relatively low.

Hence, the variance of 1 means that the values of the given data set are relatively more than the expectations.

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The number of students taking classes at Zeke's Karate altogether is 108 students.

Given that, at Zeke's Karate, there are 5 times as many youth students as adult students taking classes this session.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The ratio of youth students to adult students is x:5x.

If there are 72 more youth students than adult students this session

So, 5x=x+72

⇒ 5x-x=72

⇒ 4x=72

⇒ x=18

Now, 5x=5×18 =90

Total students = 18+90=108

Therefore, the number of students taking classes at Zeke's Karate altogether is 108 students.

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In general, the duration of a bank's zero-coupon securities with short maturities is lower than the duration of its zero-coupon securities with long maturities.

Bonds with no interest payments are those whose face value is paid back at maturity. The phrase "zero-coupon bond" refers to a bond that does not have so-called coupons or periodic interest payments like conventional bonds do. The investor of the bond receives the bond's par value when it matures. Bonds with zero coupon rates do not accrue interest throughout the course of their lifetime. Instead, buyers purchase zero-coupon bonds at a significant discount to face value, which represents the sum the buyer will get when the bond "matures" or becomes due.

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Possible combinations that can be formed a committee of 5 male and 2 female with at least 3 men that must be at the committee from 13 members is 28000.

What is combination?

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

C (n, r) = n! (r! n-r!)

According to the given question:

8 males, 3 at a time = Comb (8,3) = 56

5 females, 2 at a time = Comb (5,2) = 10

So, the base combination of 5 males & 2 females from 8 possible males and 5 possible females = 56 x 10 = 560.

However, the total combinations are further expanded by the condition that 3, 4 or 5 of the 5 male members must be present

This expansion factor is the Comb (5,3) x Comb (5,4).

So, Comb (5,3) x Comb (5,4) = 10 x 5 = 50

Therefore, the combined total are 560 x 50 = 28,000 possible combinations of 5 of 8 possible males & 3 females of 5 possible females with 3, 4 or 5 of the males being present.

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If the data collection contains the following numbers: 3, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85 , Here 3 and 85 represents the outlier.

The important characteristics of Statistics are given as follows:

Outliers are the data's most wildly divergent values.

For instance, if the data collection contains the following numbers: 3 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85

The display of data and outliers

The numbers 3 and 85, which are at the extremes and are hence outliers in the number line above, may be seen to be at these extremes.

The group's outliers are a part of it, but they are not close to the other group members.

Outliers are a concern since they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.

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Radius defines the length between the center and corner point of the circle.

Circle:

Circle means a round shape that has no corners or line segments and it is  a closed curve shape in geometry.

Given,

Here we have to define what is radius

As per the concept of the circle, radius is the half of the diameter.

Where the diameter a line segment through the center of a circle with its ends on the circle's circumference.

And the radius refers the straight line from the center to the circumference of a circle or sphere.

In order to find the radius, simply divide the diameter by 2.

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ASA congruence postulate says that if the two angles and the included side of a triangle are congruent to two angles and the included side of another triangle then the triangles are congruent. ABC ≅ XYZ

Congruent triangles are those with precisely the same dimensions and appearance. Congruent has the symbol. When the dimensions of one triangle's three sides and three angles match those of another triangle's three sides and three angles, the two triangles are said to be congruent.

Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below.

According to the ASA criterion, ABC = XYZ because BC = YZ and B = Y and C = Z, respectively. Due to the fact that ABC = XYZ, the third angle (A) and the other two sides (A) of ABC must be equal to the equivalent angle (X) and sides of XYZ.

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The total amount of money that the employee made was $400.58

What is the hourly rate?

The amount that is paid per hour of work is known as an hourly rate.

The hourly rate can be calculated by:

The total amount of pay = hours worked * hourly rate of pay

Given, the rate per hour = ​$9.94

Total work duration = 40.3 hours

Now,

The total amount that the employee​ makes = ​$9.94*40.3 = ​$400.58

Hence, the employee​ made $400.58.

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The probability that the center is up when the person’s call comes in is 2/5

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Let us consider a random variable Y it presents the number of person’s call comes when center is up. Beginning at 12:00 midnight, a computer center is up for 1 hour and then down for 2 hours on a regular cycle.

We need to find  the probability that the center is up when the person’s call comes in.

Let 12:00 midnight be ‘a = 0’, then we will have ‘b = 5’, therefore f(y) = 1/5

For beginning of a = 0, the computer is up for 1 hour, so P(0<Y<1)

The computer is down for 2 hours and then up for another one hour, so P(3<Y<4)

Hence,

The probability that the center is up when the person’s call comes in is given by:

P(0<Y<1) + P(3<Y<4) = ∫f(y) dy + ∫f(y) dy

= (1/5)y + (1/5)y

= (1/5)((1-0)+(4-3))

= 2/5

Therefore, The probability that the center is up when the person’s call comes in is 2/5

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The given function is f(x) = 1/x - 1, with x and y intersecting (1,0) and the graph is attached below.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The given function is f(x) = 1/x - 1

f(x) = 1-x / x

Now put x = 0 to get the y-intercept

f(x) = ∞

It doesn't touch y-axis.

Putting f(x) = 0

1-x /x = 0

⇒1-x = 0

⇒x = 1

So the x-intercept is 1.

Hence, is f(x) = 1/x - 1, with x and y intersecting (1,0) and the graph is attached below.

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Answer:The SAS criterion for triangle congruence states that if two triangles have two pairs of congruent sides and the included angle (the one between the congruent sides) in one triangle is congruent to the included angle in the other triangle, then the triangles are congruent.

Step-by-step explanation:

How do you prove two triangles are congruent using SAS?

SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.

How can you determine if the two triangles are congruent?

So we know that two triangles are congruent if all of their sides are the same-- so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.

The greatest common divisor(GCD) of 10 and 50 is 10.

The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.

In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.

Foe calculating the GCD of 10 and 50, we have to find the factors of 10 and 50.

Factors of 10:

1, 2, 5, 10

Factors of 50:

1, 2, 5, 10, 25, 50

From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 50 are 1, 2, 10, and 5.

So, the greatest factor of 10 and 50 is 10.

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The Area of Face A is 12 m² and face B is 18 m² and face C is 54 m².

Area is a measure of the amount of space enclosed by a two-dimensional shape or surface. It is a fundamental concept in geometry and is expressed in square units.

We have,

length = 9m

width = 6 m

height = 2m

So, the Area of face A

= l w

= 6 x 2

= 12 m²

and, area of Face B

= 9 x 2

= 18 m²

and, Area of face C

= 9 x 6

= 54 m²

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When the scale factor is greater than 1, the image is larger than the pre-image.

Dilatation is a transformation that modifies a figure's size without changing its shape. Due to dilatation, a figure may grow or shrink. The preimage refers to the first figure in dilatation. It shows an expanded figure. Figures are warped from a fixed point called the center of dilatation.

When you enlarge or reduce a figure, the scale factor indicates how much smaller or larger the result will be.

• When the scaling factor is between 0 and 1, the picture is smaller than the preimage. On a scale of 0 to 1, dilations are referred to as reductions.

• If the scale factor is more than 1, the image is bigger than the preimage. The definition of enlargement is a dilatation with a scale factor higher than 1. Each new point in a dilated figure is denoted by the prime sign, ". As an illustration, point', which denotes "prime," would be the enlarged version of point.

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