Use technology or a z-score table to answer the question.
The scores on a memory test are normally distributed with a mean of 100 and a standard deviation of 25. Consider a group of 400 people who take the test.

How many people will score 90 or less?

63

138

180

262

If the two sides on one triangle are congruent to the corresponding two sides of the other triangle and the included angles are congruent in both triangles, then the triangles are congruent by SAS (side-angle-side).

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.

Use the SAS theorem of congruence to determine if the triangles in the figure below are congruent.

From fig(1) is congruent to fig(2).

For each triangle, find two labeled sides with labeled included angle (side-angle-side in order).

For ΔABC, we have:

|AC|=10,m∠A=46∘, |AB|=7

For ΔXYZ, we have:

|XZ|=10,m∠Z=46∘, |YZ|=7

Compare the results from step. If the two sides on one triangle are congruent to the corresponding two sides of the other triangle and the included angles are congruent in both triangles, then the triangles are congruent by SAS.

So, |AC|=|XZ|, m∠A=m∠Z, |AB|=|YZ| the triangles are congruent by SAS.

For more such questions about side-angle-side.

https://brainly.com/question/29124246

#SPJ4

x=1/2 and x=-4 are zeros of the polynomial 2x²+7x-4=0.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is 2x²+7x-4=0

To find the zero of 2x²+7x-4=0 we need to find the roots of polynomial.

2x²+7x-4=0

2x²+8x-x-4=0

Take 2x as common from first two terms

2x(x+4)-(x+4)=0

(2x-1)(x+4)=0

2x-1=0

2x=1

x=1/2 and x=-4 are zeros.

Hence, x=1/2 and x=-4 are zeros of the polynomial 2x²+7x-4=0.

To learn more on Polynomials click:

https://brainly.com/question/11536910

#SPJ4

Answer:

Below

Step-by-step explanation:

1/a + 1/r = 1/3        a = aaron rate   r = rosa rate    3 = rate of both

1/5 + 1/r = 1/3

1/r = 2/15

r = 15/2 = 7.5 hr for rosa alone

Answer:

11.1

Step-by-step explanation:

sin 46 · x = 8

0.71934 x = 8

x  = 8/0.71934

x = 11.121306

Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

Now, According to the question :

Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1,2,3,4,5,6,7,8,…..∞}. Also, check sets here.

Sets can be represented in three forms:

1. Roster Form: Example- Set of even numbers less than 8={2,4,6}

2. Statement Form: Example-A = {Set of Odd numbers less than 9}

3. Set Builder Form: Example: A = {x: x=2n, n ∈ N and 1 ≤ n ≤ 4}

What are the types of Sets?

A set has many types, such as;

1. Empty Set or Null set

2. Finite Set

3. Infinite Set

4. Equal Set

5. Subsets

6. Universal Set

Learn more about Sets at:

https://brainly.com/question/27743632

#SPJ4

The number of choices the gardener has is 440440

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The formula for combination is [tex]^nC_r[/tex] = n! / r!(n - r)1

We have,

Number of geranium = 14

Number of lilies = 12

Number of geranium bought = 5

Number of lilies bought = 3

The number of choices.

= [tex]^{14}C_5 \times ^{12}C_3[/tex]

= (14 x 13 x 12 x 11 x 10)/(5 x 4 x 3 x 2) x (12 x 11 x 10)/(3 x 2)

= 14 x 13 x 11 x 2 x 11 x 10

= 440440

Thus,

The number of choices is 440440.

Learn more about combination here:

https://brainly.com/question/14355408

#SPJ1

The graph of linear inequalities is straight line bounded by solid or dashed region.

The graphing system of linear inequalities is different from linear eqaution because of  using equal to inequal sign such as ≥ and ≤ or inequal sign < and >.

when we plot the poins on XY axis we get a straight line. The region that satisfy the inequalities of variables are bounded by either solid line or dashed line.

hence, the graphing system of linear variables has shaded portion where straights line is the boundary.

to read more about graphing system visit:

https://brainly.com/question/25168368

#SPJ4

Answer:

Hence, x=28.

Step-by-step explanation:

Both median and mean originate from the Latin medianus, meaning in the middle, the former by way of the Anglo-French meiene. Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest.  

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed.

The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.

This is why it is called a median.

To learn more about median, visit the link:

brainly.com/question/28060453

#SPJ4

The approximate volume of the greenhouse will be 1,527 ft³.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Ellen's greenhouse is in the shape of a hemisphere.

And, The diameter of the floor is 18 feet.

Now,

Since, Ellen's greenhouse is in the shape of a hemisphere.

We know that;

⇒ The volume of Hemisphere = (2/3) πr³

Here, The diameter of the floor is 18 feet.

Hence, The radius of the floor = 18/2

                                               = 9 feet

So, We get;

⇒ The volume of Hemisphere = (2/3) πr³

⇒ The volume of Hemisphere = (2/3) × 3.14 × 9³

                                               = 1,527 ft³

Thus, The approximate volume of the greenhouse =  1,527 ft³

Learn more about the multiplication visit:

https://brainly.com/question/28768606

#SPJ1

you will find that the slope, or m, is equal to 4/5 and that b is the coordinates 0 and -4

What is the slope of the relation y 4 5x 4?

The first step that needs to be done is to convert the equation into the y=mx+b format where m is the slope and b is the intersection of the y-intercept. Simply solve the equation for Y and you get Y=4/5X-4. From this, you will find that the slope, or m, is equal to 4/5 and that b is the coordinates 0 and -4

if the slopes are:

L1: slope 3

L2: slope -3

L3: slope -1/3

So now multiply the slopes of each pair of lines:

L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular

L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular

L1 and L3: (3) *  (-1/3) = -1 => Yes, they are penpendicular.

learn more about of slope here

https://brainly.com/question/3605446

#SPJ4

Answer:

B

Step-by-step explanation

Multiplying by 0.97 will decrease $200,000 to $194,000.

^c is x years after the purchase, so having (0.97)^c will make the $200,000 value decrease more and more.

The given values are 2,6,5,3,0,3,4,3,2,4,5,2,4

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 2-3 the number 2 appears only Three times.

2. 6-1 the number 6 appears one time.

3. 5-2 the number 5 appears only two times.

4. 3-3 the number 3 appears only three times.

5. 0-1 the number 1 appears only one time.

6. 4-3 the number 4 appears only Three times.

So, the mode of the given data is 4,3,2 as it appears the most number of times.

If a given set of values with two modes is bimodal, a given set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.

To know more about Mode:

https://brainly.in/question/19575343

#SPJ4

The value of x is x=34.

What is angles?

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 on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The angles are corresponding angles so they are equal if m is parallel to n

x+27 = 2x -7

Subtract x from each side

x+27 -x =2x-x-7

27 = x-7

Add 7 to each side

27+7 = x-7+7

34 =x

To learn more about angles visit:https://brainly.com/question/28451077

#SPJ1

Answer:

Step-by-step explanation:

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

Integral is a term derived form the word integration. Integration in calculus is the opposite of differentiation

Integration is used to get the whole by combining combine slices or smaller portions.

Finding areas, volumes, central points, and many other important things may be done with integration. However, it is simplest to begin by calculating the distance between a function and the x-axis.

Learn more about integral at:

https://brainly.com/question/27419605

#SPJ1

Answer:

4xyxy

Step-by-step explanation:

there is a baby 2 so add 2 more x and y. ;)

b. if two parallel lines are cut by a transversal, then corresponding angles are congruent.

c. if two parallel lines are cut by a transversal, then alternate interior angles are congruent.

d. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

Answer:

  d.  f(x) → +∞, x → +∞; f(x) → -∞, x → -∞

Step-by-step explanation:

You want the end behavior of the cube root function f(x) = 2∛x +3.

The vertical translation upward 3 units can be ignored when considering the end behavior. The sign of a cube root matches the sign of the argument, so the signs of x and f(x) will match when both get large.

  f(x) → +∞, x → +∞; f(x) → -∞, x → -∞

The solution of the given system of equations 3x + y = 10 ,  x - y = 2 is equal to x = 3 and y = 1.

As given in the question,

Given system of equations are :

3x + y = 10      ____(1)

x - y = 2    _____(2)

Add equation (1) and  (2) to eliminate y and get the value of x we have,

3x + y = 10

x - y = 2

4x      = 12

⇒x = 12 / 4

⇒ x = 3

Substitute value of x = 3 in equation (1) to get the value of y for the given equation,

3(3) + y = 10

⇒ 9 + y = 10

⇒ y = 10 - 9

⇒ y = 1

Therefore, the solution of the given system of equations is equal to x = 3 and y =1.

The above question is incomplete, the complete question is:

What is the solution of the system of equations 3x + y = 10 ,  x - y = 2?

Learn more about system of equation here

brainly.com/question/12895249

#SPJ4

The yield of stock at yesterday's closing price is 3.43%.

Annual dividend is the profit of the stock which is divided among the shareholders, both common and preferred shareholders annually.

Given,

Annual dividend = $1.20

Today's closing price = $34.50

Net change = -$0.50

Let x be yesterday's closing price.

Net change = Today's closing price - yesterday's closing price

⇒ -0.50 = 34.50 - x

⇒ x = 34.50 + 0.50

⇒ x = 35

Yield = [tex]\frac{Annual dividend}{Price}[/tex] × 100

         = [tex]\frac{1.2}{35}[/tex] × 100

         = 3.4286 % ≈ 3.43 %

Hence the stock's yield at yesterday's closing price of preferred stock is 3.43 %.

Learn more about Annual Dividend here :

https://brainly.com/question/15871366

#SPJ4

The expected number that will arrive on time is; 151.23

The standard deviation of this distribution is; 6.62

We are given;

Percentage of the flights involved in the study arrived on time; p = 71% = 0.71

Sample size; n = 213

Now, the formula for the mean which is the expected number that will arrive on time is;

μ = np

μ = 213 * 0.71

μ = 151.23

The formula for the standard deviation of the distribution is;

σ = √(np(1 - p))

σ = √(213*0.71(1 - 0.71))

σ = 6.62

Read more about mean and standard deviation at; https://brainly.com/question/26941429

#SPJ1

you can rent the boat 55.92 hour if It costs $$3535 per hour to rent a boat at the lake. You also need to pay a $$2525 fee for safety equipment.

What is an example of an equation?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

It costs $$3535 per hour to rent a boat at the lake.

You also need to pay a $$2525 fee for safety equipment.

You have $$200200.

safety fee only once

so 200200-2525 = 197675

if one hour fees is 3535

then 197675/3535

= 55.92

hence he rent boat at the lake 55.92 hour

learn more about of equipment here

https://brainly.com/question/17096601

#SPJ4

Addition, subtraction, multiplication and division are four type of arithmetic

Beside mentioned above exponential and modulus operations are also arithmetic

The Greek noun arithmos, which means "number," is where the word arithmetic ultimately comes from. Along the way, it also appeared in Latin, Anglo-French, and Middle English. Even elementary mathematics has a rich vocabulary. Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations.

So addition,multiplication, subtraction and division are 4 types of arithmetic

2+2=4

2*2=4

2/2=1

2-2=0

To learn more about arithmetic visit the link:

https://brainly.com/question/24989563

#SPJ4

Table a and table c defines a relationship between an input x and an output y of function.

A function is a set of ordered pairs (x, y) in which each value of x corresponds to exactly one value of y. In other words, for a given value of x, there should be only one corresponding value of y.

Looking at the tables, we can see that Table a and Table d both satisfy this condition. In both tables, for each value of x, there is only one corresponding value of y. Therefore, Tables a and d represent functions.

Table b and Table c do not satisfy this condition, because there are multiple values of y for some of the values of x.

For example, in Table b, the value of x is 24 for both (24, 53) and (24, 29). Similarly, in Table c, the value of x is 24 for both (24, 53) and (24, 29). Therefore, Tables b and c do not represent functions.

Therefore table a and table c represents function of input x and output y.

To know more about function visit :

brainly.com/question/5975436

#SPJ4

A function is a collection of ordered pairs (x, y) where each x-value is matched up with exactly one y-value. In other words, there should only be one value of y that corresponds to a certain value of x.

We can see from the tables that Tables a and Table d both meet this requirement. In both tables, there is only one value of y that corresponds to each value of x. Tables a and d so depict functions.

Because there are many possibilities of y for some of the values of x, Tables b and c do not meet this requirement.

For instance, the value of x in Table b is 24 for both (24, 53) and (24, 29). The value of x is 24 in Table c for both (24, 53) and (24, 29). Tables b and c do not, therefore, represent functions.

Tables a and c therefore show the function of input x and output y.

The law of cosines generalizes the Pythagorean formula to all triangles. It says that c^2, the square of one side of the triangle, is equal to a^2 + b^2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

c^2=a^2 + b^2 - 2abcosC

Pythagorean formula

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Learn more about Pythagoras theorem here :-

https://brainly.com/question/343682

#SPJ4

The required real proportion's 95% confidence interval is (0.301; 0.359).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

So, the sample size is 1000.

Phat = 0.33

(1 - phat) = 1 - 0.33 = 0.67

Zcritical = 1.96 at 95%

The confidence range is as follows:

Phat ± margin of error

Margin of Error = Zcritical * sqrt[(phat(1 - phat)) /n]

Margin of Error = 1.96 * sqrt[(0.33 * 0.67) / 1000]

Margin of Error = 1.96 * 0.0148694

Margin of Error = 0.0291440

Lower boundary = (0.33 - 0.0291440) = 0.300856

Upper boundary = (0.33 + 0.0291440) = 0.359144

Therefore, the required real proportion's 95% confidence interval is (0.301; 0.359).

Know more about the confidence interval here:

https://brainly.com/question/15712887

#SPJ4

Correct question:
Cyber Monday Shopping A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion.

There are three types of roots in mathematics which are real , repeated and non real roots.

When the value of the roots obtained are less than 0 then the roots obtained are known as not real or imaginary roots.

When the roots are greater than zero then they are known as real roots.

When the value of roots obtained is equal to 0 then we conclude that the roots are repeated.

We can get the roots of a function by factorizing the given expression or we can also find them using the determinant method. Or we can also use the graphical method to find the roots.

To learn more about roots

brainly.com/question/29755184

#SPJ4