PROBLEM 1
Adrian said that g(x) = x +41 ls
translated up 4 units from the parent
function f(x) = |xl.
Do you agree or disagree? Why?
PROBLEM 2
Ezra determined that the graph
shown below is vertically
compressed by a factor of from the
graph of y= |x|.
Do you agree or disagree? Why?

The probability of acceptance of Jim at both the University as per given acceptance rate is equal to 0.135.

As given in the question,

Acceptance rate of Jim application at University x is equal to 30%

Acceptance rate of Jim application at University y is equal to 45%

Probability of acceptance of application in University x is:

P(x) = 30 /100

      = 0.30

Probability of acceptance of application in University y is:

P(y) = 45 /100

      = 0.45

Probability of acceptance of application at both the University is:

P(x and y) = P(x) × P(y)

                = 0.30 × 0.45

                = 0.135

Therefore, the probability of acceptance application at both the University is equal to 0.135.

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The value of a is 42.

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex](15-a)/3=-9[/tex]

or, [tex]15-a=-9*3[/tex]

or,[tex]-a=-27-15[/tex]

or, [tex]a=42[/tex]

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Answer:

A= -5

B= -10

c= 4

Step-by-step explanation:

hope this helps

Answer:

a) -5

b)-10

c) 4

Hope this helps!

The probability that at least 5 will do their homework on time in a class of 50 students is 0.1

Probability

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.

the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.

Each student does homework independently.

In a statistics class of 50 students, what is the probability that at least 5 will do their homework on time.

Probability = event occur/ total number of outcomes

                  = 5/50= 1/10=0.1

Thus the probability becomes 0.1

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Answer:

(2 (3 i + 1))/5

Step-by-step explanation:

Simplify the following:

(4 i)/(i + 3)

Multiply numerator and denominator of (4 i)/(i + 3) by 3 - i:

(4 i (-i + 3))/((i + 3) (-i + 3))

(3 + i) (3 - i) = 3×3 + 3 (-i) + i×3 + i (-i) = 9 - 3 i + 3 i + 1 = 10:

(4 i (-i + 3))/10

The gcd of 4 and 10 is 2, so (4 i (-i + 3))/10 = ((2×2) i (-i + 3))/(2×5) = 2/2×(2 i (-i + 3))/5 = (2 i (-i + 3))/5:

(2 i (-i + 3))/5

i (3 - i) = 1 + 3 i:

Answer: (2 (3 i + 1))/5

Answer: below

Step-by-step explanation:

A. x=20+2n n= number of months

y=10(1+0.15)^n

B.

x 20,22,24,26,28,30....40

y 12.5,13.225,15.2,....40.5

C. The solution is 11 months because at 10 months even though the number of animals surpass the number of homes, you cannot have half a animal.

D.

Answer:

96 dollars

Step-by-step explanation:

The ratio of Miguel's savings to his earnings is 8: 10 = 40: 50 = 120: 150 is equal to ratio 4:5

If Miguel earns $120, then he will save 4/5 of his earnings.

This can be expressed as a ratio as follows:

Savings: Earnings = 4 : 5

This means that for every 4 units of savings, there are 5 units of earnings. In other words, the ratio of savings to earnings is 4 to 5.

In order to calculate the amount of money that Miguel will save; we can multiply the ratio by the amount of earnings.

In this case, the amount of earnings is $120, so the amount of money that Miguel will save is:

[tex]\textsf{Savings} =\dfrac{ 4}{5 }* 120 = 96[/tex] dollars

Therefore, He will save 96 dollars if he earns 120 dollars.

The given statement is true. The example is 40° and 50°.

What is counterexample?

An example that satisfies the condition(s) of a mathematical statement but does not result in the conclusion of the statement is referred to as a counterexample.

What is angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

If the sum of two angles is 90°, then the angles are complementary angles each other.

40° and 50° both angles are less than 90°.

The sum 40° and 50° is 90°.

Thus, 40° and 50°  are complementary to each other.

Therefore the given statement is true.

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The required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

Given that,
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
let y be the total cost for each different item
cost of the shirt = s - 10 and pair of pants = 2p
According to the question,
y = s - 10 / 2  and y = 2p / 2

Thus, the required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

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The first error Bailey made was in the justification for his initial statement. The correct term to use is reflexive property.

An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.

If A is an angle, then A is an angle.

Angle A intersects Angle A.

An angle will always be equal to or congruent to itself, according to the reflexive property of congruence.

So, for instance, given an angle, B, so:

∠B ≅ ∠B

Based on the reflexive property of congruence and the illustration provided:

∠F ≅ ∠F

Therefore, the first error Bailey made was in the justification for his initial statement. The correct term to use is reflexive property.

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Complete question;
Bailey tried to prove that FGJ~FHI in the following figure, but her proof is wrong. What is the first mistake Bailey made in the proof?

From the given information in question, we can sat that, The  regular polyhedron have 30 edges.

A polygon that is based on the solid in the three dimensions is known as  a polyhedron. It has flat faces, straight edges and corners. A polyhedron is something like a cube, prism, or pyramid. Cones, spheres, and cylinders do not have polygonal sides, hence they are not polyhedra. Polyhedron is also the name of the polyhedron's plural form. They are classified as prisms, pyramids, and regular polyhedra. Polyhedra include, for instance, cubes (regular polyhedrons), square prisms, triangular prisms, square pyramids, and square pyramids. Consider the diagram below displaying different sorts of polyhedra.

chris discovered that the centers of the faces of a regular icosahedron are also the vertices of another regular polyhedron and he  regular polyhedron have 30 edges.

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The statement made by Erin about the triangles is false

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

As a general rule of dilation (i.e. scale factors),

The area of the image of the dilation is the square of the scale factor multiplied by the area of the pre-image shape

Mathematically, this is represented as

Area of the image of the dilation = scale factor² * Area of the pre-image shape

Using familiar terms, we have

Area of ∆XYZ = (31)² * the area of ∆ABC.

The above statement is true and it is not the same as Erin's statement

Hence, Erin is incorrect

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Answer:

1. 45*4 = 180
2. 65*5= 325
3. 77*6=462
4. 89*7= 623

5. 52*3= 156

Answer:

5.8

13.25

22.62

34.23

16.56

Step-by-step explanation:

Answer: 69/20

Step-by-step explanation:

5 1/5 = 26/5

1 3/4 = 7/4

26/5 - 7/4

= 104/20 - 35/20

= 69/20

The number of cups that will be in 3 gallons is 48 cups.

It is important to note that ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Based on the information, the number of cups won a gallons will be:

= 64 / 4

= 16 cups.

Therefore, the cups that will be in 3 gallons will be:

= 3 × 16. cups

= 48 cups.

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The algebraic expression for "9 less than the quotient of z and 8" exists 9 - z / 8.

Using variables, constants, and algebraic operations, an expression can be described as an algebraic expression in mathematics (addition, subtraction, etc.). Terms are used to construct expressions.

Similar to this, when we describe an algebraic expression in English and it has a variable, we are doing so (an expression with a variable).

A mathematical expression made composed of integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Let the given expression be "9 less than the quotient of z and 8".

simplifying the expression, we get

= 9 - z / 8

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As per the given confidence interval, the interval notation is 2.576

Confidence interval:

Is statistics, an estimate of an interval in statistics that may contain a population parameter is known as confidence interval.

Given,

Here we have to calculate a 99% confidence interval for the difference in the proportions of those older than 30 and those 30 or younger that believe alcoholic beverage commercials targeted teenagers and young adults. let the 30 or younger age group be population 1 and let the older than 30 age group be population.

And we need to find the write your answer using interval notation and round the interval endpoints to three decimal places.

While we looking into the given question,

We have identified the following things,

Confidence interval = 99%

When we convert this into decimal, then we get the value as 0.99

Then the z score of the given data is calculated as

=> 2.576

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Answer:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

Step-by-step explanation:

Apply natural logarithm chain rule:

[tex] \displaystyle{y = \ln(u) \to y' = \dfrac{u'}{u}}[/tex]

Where u is a function. The ' symbol indicates that the function to be derived. From this formula, we will have:

[tex] \displaystyle{y' = \dfrac{ \left (\dfrac{1 + x}{1 - x} \right)'}{ \dfrac{1 + x}{1 - x}}}[/tex]

Now we have to derive quotient functions, we can use quotient rule for this:

[tex] \displaystyle{y = \dfrac{u}{v} \to y' = \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

Where u and v are functions. Therefore, from numerator:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{(1 + x)'(1 - x) - (1 + x)(1 - x)'}{ {(1 - x)}^{2} }}[/tex]

Derive using power rule and constant rule where:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: \: ( c \in \mathbb{R})}[/tex]

Thus:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1(1 - x) - (1 + x)( - 1)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x- ( - 1 - x)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x + 1 + x}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{2}{ {(1 - x)}^{2} }}[/tex]

Therefore, we will now have:

[tex] \displaystyle{y' = \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}}}[/tex]

Simplify expressions:

[tex] \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ {(1 - x)}^{2}} \times \dfrac{1 - x}{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ 1 - x} \times \dfrac{1 }{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ (1 - x)(1 + x)}}[/tex]

Therefore, the derived function is:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

The radius of the circular garden is 14.3 meters

Any line connecting a circle's center and circumference is said to be the circle's radius. Within a circle, a diameter is equal to the sum of two radii. The area and circumference of a circle are determined using the radius of the circle.

The perimeter of a circle with a radius of r is given by

Here we have

George walks around one-quarter of a quarter of a circular garden.  

He walks a total of 30 meters.

Let x be the Perimeter or circumference of the circular garden

Given that George walks around one-quarter of a quarter of a circular garden.

=> The length of the path that George walked = x/3

Given that He walks a total of 30 meters

=>  x/3 = 30 meters

=>  x = 90 meters

So we can conclude that circumference of the circular garden = 90 m

As we know Perimeter of the circle = 2πr  

=> 2πr = 90

=>  πr = 45

=> 22/7(r) = 45

=> 22(r) = 315

=> r = 14.318181818181 ≅ 14.3

Therefore,

The radius of the circular garden is 14.3 meters

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Answer: 61.9%

Step-by-step explanation:

First, add 16 and 26 together to get the total of chicken = 42

Then take 26 divided by 42, then times 100% = 61.9%

Answer:

w = [tex]\frac{20}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] w = 4 ( multiply both sides by 5 to clear the fraction )

3w = 20 ( divide both sides by 3 )

w = [tex]\frac{20}{3}[/tex]

Answer:

-------------------------------------------

The first number is:

And the second number is -3.4.

Both numbers are rational, hence their product is rational.

Answer:

Rational as it is a terminating decimal.

Step-by-step explanation:

Given expression:

[tex]\sqrt{1024} \cdot -3.4[/tex]

Rewrite 1024 as 32²:

[tex]\implies \sqrt{32^2} \cdot -3.4[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies 32 \cdot -3.4[/tex]

Multiply the numbers:

[tex]\implies -108.8[/tex]

Therefore, the product is a terminating decimal.

A rational number is a number that can be expressed as the ratio of two integers (where the denominator does not equal zero).  

A terminating decimal can be written as a rational number.

To convert a terminating decimal into a rational number, multiply the number by a multiple of 10 that eliminates the decimal, then divide by the same number:

[tex]\implies \dfrac{-108.8 \cdot 10}{10}[/tex]

[tex]\implies -\dfrac{1088}{10}[/tex]

Reduce the fraction to its simplest form by dividing the numerator and denominator by 2:

[tex]\implies -\dfrac{544}{5}[/tex]

Therefore, the product of √1024 and -3.4 is rational as it is a terminating decimal.

The no. of groups of five can be chosen that contain at most three women is 60.

The method we use to solve this is combination method.

Mathematical combinatorics is a division that deals with counting.

Combinatorics can assist us in counting the possible sequences in which something can occur.

Numerous applications of combinatorics can be found in other branches of mathematics, such as graph theory, coding and cryptography, and probability.

In mathematics, you can also have combinations, such as linear combinations or combinations of functions.

To solve this we use combination method of mathematics

The no. of groups of five can be chosen is

⁵C₃ * ⁴C₂

⇒ (5 * 4 * 3! / 3! * 2!) * (4 * 3 * 2! / 2! * 2!)

⇒ (5 * 4 / 2 * 1) * (4 * 3 / 2 * 1)

⇒ 5 * 2 * 2 * 3

⇒ 60

The no. of groups of five can be chosen that contain at most three women is 60.

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The angle between the ladder and the ground is - 0.075 rad/s.

Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative  facets.

cosθ = x/10

On differentiating the above equation,

- sinθdθ/dt = (1/10)dx/dt

dθ/dt = -(1/10)dx/dt/sinθ

sinθ = y/10

= √(100 - 36)/10

= 0.8; dθ/dt

= -(1/10)·0.6 ft/s/0.8

= - 0.075 rad/s

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Number of ways can this company buy them is 1623160.

Given :

a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees.

Number of ways = [tex]35_C_6[/tex] or C ( 35 , 6 )

we know that ,

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

substitute

= 35 ! / ( 35 - 6 ) ! 6!

= 35 * 34 * 33 * 32 * 31 * 30 * 29! / 29! * 6!

= 35 * 34 * 33 * 32 * 31 * 5 / 5 * 4 * 3 * 2 * 1

= 35 * 17 * 33 * 32 * 31 / 4 * 3

= 35 * 17 * 11 * 8 * 31

= 1623160 ways

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Answer:

x = -3

Step-by-step explanation:

Welcome to Brainly! :]

3/4(x-13)=-2(9+x)

0.75x - 9.75 = -18 - 2x

2.75x = -8.25

x = -3

:]

The value after double integration is 45.73

We can evaluate rectangle integrals in any order we like in Cartesian coordinates. We treat the other integral as a constant regardless of which integral we assess first; this is something to keep in mind while choosing the order of integration.

We want that x to be constant; we can easily integrate with respect to y. So we will evaluate y first. We get:

[tex]\int\limits^ \int\limits^ \frac{6x}{1+xy} dA=6\int\limits^6_0 \int\limits^1_0 {\frac{x}{1+xy} } \, dydx[/tex]

[tex]or, 6\int\limits^6_0 {[In(1+xy)}_{0} ^{1} ]} \, dx[/tex]

[tex]or, 6\int\limits^6_0 {In(1+x)} } \, -In 1dx[/tex]

[tex]or, 6\int\limits^6_0 {In(1+x)} } \, dx[/tex]

[tex]or,[(1+x)In(1+x)-(1-x)]^{6} _{0}[/tex]

[tex]or,[7In7-In1-7+1]\\or,6(7In7-6)\\or,45.73[/tex]

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Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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The happening in the graph is that the speed of the roller skater increases and decreases with time

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

The graph

On the graph, we have the following axes

x-axis = Time

y-axis = Speed

The x-axis is continually increasing while the y-axis decreases and increases (as in a sine function)

This means that the speed increases and decreases with time

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