Use the normal distribution to the right to answer the questions. (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? Standardized Test Composite Scores 1921Score mu equals 19.6 sigma equals 5.3 mu x A graph titled "Standardized Test Composite Scores" has a horizontal x-axis labeled "Score" from about 1 to 38 with tick marks at 19 and 21. A normal curve labeled μ = 21.2 σ = 5.4 is centered above the x-axis at 21.2. A vertical line segment labeled μ extends from the normal curve to the x-axis at 21.2. (a) The percent of scores that are less than 19 is nothing %. (Round to two decimal places as needed.) (b) About nothing scores would be expected to be greater than 21. (Round to the nearest whole number as needed.)

Answer:

To apply the distributive property using the greatest common factor (GCF) to write an equivalent expression for 0.3x - 2.7, we need to find the GCF of the coefficients of the terms in the expression. In this case, the GCF is 0.3, so we can write the expression as 0.3(x - 9). This is an equivalent expression to 0.3x - 2.7, because multiplying 0.3 by the difference of x and 9 produces the same result as subtracting 2.7 from 0.3x.

Step-by-step explanation:

The proof that shows that ΔLMN ≅ ΔQPN by either SSS or SAS is explained below.

If we can show that two triangles have two pairs of congruent sides and a pair of corresponding congruent included angles, then we can state they are congruent triangles based on the SAS theorem.

On the other hand, if all three corresponding side lengths are congruent to each other, then the triangles are congruent by the SSS theorem.

The proof that can be used to show that the two triangles are congruent by SAS is shown below:

Statement                                 Reasons                                  

1. ∠L ≅ ∠Q, LM ≅ QP,              1. Given

MN ≅PN, NL ≅ NQ

2. ΔLMN ≅ ΔQPN                    2. SSS

Based on the given information we are given, another way of writing this proof can be:

Statement                                 Reasons                                  

1. ∠L ≅ ∠Q, LM ≅ QP,              1. Given

MN ≅PN, NL ≅ NQ

2. ΔLMN ≅ ΔQPN                    2. SAS

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Answer:

29

he area of the pool is 34 ft * 48 ft = <<34*48=1632>>1632 ft2.

Thus, the total area of the pool and the border strip is 1632 ft2 + 344 ft2 = <<1632+344=1976>>1976 ft2.

Hence, the border strip is 1976 ft2/34 ft = <<1976/34=58>>58 ft long.

Therefore, the border strip can be 58 ft/2 = <<58/2=29>>29 ft wide. Answer: {29}.

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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Reason:

x and y are the legs.

[tex]5\sqrt{2}[/tex] is the hypotenuse.

The hypotenuse is always opposite the 90 degree angle.

The hypotenuse is always the longest side of any right triangle.

Answer:

27a + 72

Step-by-step explanation:

Open the brackets

9(3a) + 9(8)

27a +72

Answer:

27a + 72

Step-by-step explanation:

9(3a + 8)

Using the distributive property, we can multiply 9 by everything in parentheses, which now gives us: 27a + 72

We cannot simplify this further, as we have an unknown value in the variable a, thus we cannot apply 72 to 27a, or inverse.

Meaning that, the answer is 27a + 72

After solving the angles, the measure of angle x is 145°.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is where the term "angle" originates.

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.

A geometrical shape called an angle is created by connecting two rays at their termini.

In most cases, an angle is expressed in degrees.

(Refer to the image attached below)

We can see that ∠ABC is a straight angle.

∠ABC = ∠ABD + ∠DBC where ∠ABD is x.

Now, solve for x as follows:

∠ABD + ∠DBC = ∠ABC

x + 35 = 180

x = 180 - 35

x = 145°

Therefore, after solving the angles, the measure of angle x is 145°.

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The solutions for the given equation is x=0, x=-4 and x=3.

The given functions are f(x)=2x³+9x²+13x+12 and g(x)=3x³+10x²+x+8.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, f(x)-g(x)

= 2x³+9x²+13x+12-(3x³+10x²+x+8)

= 2x³+9x²+13x+12-3x³-10x²-x-8

= -x³-x²+12x+4

Graph the cubic using its end behavior and a few selected points.

Rises to the left and falls to the right

Plot (-2, -16), (-1, -8), (0, 4), (1, 14) and (2, 16)

Given f(x)-g(x)=4

-x³-x²+12x+4=4

⇒ -x³-x²+12x=0

⇒ -x(x²+x-12)=0

⇒ x=0 and x²+x-12=0

⇒ x=0 and x²+4x-3x-12=0

⇒ (x+4)(x-3)=0

⇒ x=0, x=-4 and x=3

Therefore, the solutions for the given equation is x=0, x=-4 and x=3.

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The statement that is true about the self-serve frozen yogurt store is;

Option C: The yogurt sales had a decreasing trend in the last four months of 2011

From the attached file, we see a pie chart, a graph and a table.

Now, let us access the given options;

a) The percentage that prefer chocolate = 38%

Percentage that prefer vanilla and strawberry combined = 22% + 30% = 52%.

Thus, the given statement is wrong

b) From the graph curve, we see that;

Number of units sold in November = 3000 units

Number of units sold in August = 6000 units

Difference is 3000 units and not 4000 units and so the statement is wrong.

c) We see that for the last four months the curve showed a decreasing slope which means a decreasing trend of units sold.

d) This is not correct because the median number of ounces sold from 3 to 4pm was not more than the median number of ounces sold from 7 to 8pm on the stem leaf plot.

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Answer:

To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 2.5, as it is the middle value when the data is arranged in ascending order.

Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {1.3, 1.5, 1.7, 2, 2.5}, and the upper half of the data is {2.7, 2.9, 3, 3.1}. The median of the lower half is 1.7, and the median of the upper half is 2.9.

Therefore, the value of the quartiles is Q1 = 1.7, Q2 = 2.5, and Q3 = 2.9.

Option C, Q1 = 1.7; Q2 = 2.5; Q3 = 2.9, is the correct answer.

Step-by-step explanation:

Answer:

2.95

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

The coordinates of point C is (-2, 12)

The segment OC is perpendicular to the chord AB.

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4).

C is the midpoint of the chord AB.

Now,

The coordinates of C = (x, y).

x = (-6 + 2) / 2 = -4/2 = -2

y = (10 + 14) / 2 = 24/2 = 12

(x, y ) = (-2, 12)

The relationship between chord AB and segment OC.

The segment OC is perpendicular to the chord AB.

Thus,

The coordinates of C is (-2, 12)

The relationship between segment OC and chord AB is that segment OC is perpendicular to chord AB.

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Answer:

17/6 divided by 5/3 is equal to 17/6 * 3/5, which simplifies to 51/30.

Answer:

  D(6, -2)

Step-by-step explanation:

You want the coordinates of point E in ∆DEF congruent to ∆ABC after, it has been translated 4 units to the right.

The triangle names tell us that point E is the image of point B after the translation.

Moving a point to the right 4 units adds 4 to its x-coordinate.

  B(2, -2) ⇒ E(2+4, -2) = E(6, -2)

Answer: The number of trials is limited to two.

The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

35. To find the number of gallons of gasoline used, we need to divide the number of miles traveled by the number of miles per gallon. In this case, we can let represent the number of gallons of gasoline used. We can then write the following equation to represent the situation:

27 miles/gallon * = 324 miles

To solve for , we need to divide both sides of the equation by 27 miles/gallon to get:

= 324 miles / 27 miles/gallon

This simplifies to:

= 12 gallons

36. To find the number of pounds of apples per hour, we need to divide the total number of pounds picked by the number of hours it took to pick them. In this case, we can divide 15,830 pounds by 8 hours to get:

15,830 pounds / 8 hours = 1,978.75 pounds/hour

Therefore, George Adrian picked about 1,978.75 pounds of apples per hour.

37. The equation m/5 = 50 can be used to describe how much money a quintet has to earn in order for each member to receive $50. In this equation, the variable m represents the total amount of money the quintet earns, and the number 5 represents the number of members in the quintet. The expression m/5 represents the amount of money that each member of the quintet receives, and the number 50 represents the target amount of money each member should receive.

The equation states that if the quintet earns a total of m dollars, then each member will receive m/5 dollars, which should be equal to 50 dollars. Therefore, this equation can be used to find the total amount of money the quintet needs to earn in order for each member to receive $50.

38. To estimate the solution of the equation 12x=-38, we can use the equation x=-38/12. This equation states that the solution of the given equation is equal to the negative of 38 divided by 12.

To estimate the solution, we can divide the negative of 38 by 12 to get:

x = -38/12 = -3.17

Therefore, the estimated solution is about -3.17. Note that this is just an estimate, and the exact solution may be slightly different.

Note: Please study hard in math.

Answer:The answer is 27x=324 miles

Step-by-step explanation:

The value of t for the given triangle angle will be equal to 1.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given the three angles of the triangle are 111,34, and 35t. The value of t will be calculated as,

35t + 111 + 34 = 180

35t = 180 - 111 - 34

35t = 35

t = 1

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Answer:

than twice the smaller number, what are the numbers?

Let's call the smaller number x and the larger number y. We know that x + y = 58 and y = 2x - 10. We can substitute the second equation into the first to get x + (2x - 10) = 58. Combining like terms, we get 3x - 10 = 58, which means that x = 24. Plugging this back into the equation y = 2x - 10, we get y = 48. So, the two numbers are 24 and 48.

The total distance walked in each case is given below;

Jada's pet turtle walked 10 feet, and then half that length again

Total distance = 10 + (1/2 of 10)

= 10 + (1/2 × 10)

= 10 + 5

= 15 feet

Jada's pet baby brother walked 3 feet, and then half that length again

Total distance = 3 + (1/2 of 3)

= 3 + (1/2 × 3)

= 3 + 1.5

= 4.5 feet

Jada's pet hamster walked 4.5 feet, and then half that length again

Total distance = 4.5 + (1/2 × 4.5)

= 4.5 + 2.25

= 6.75 feet

Jada's pet robot walked 1 foot, and then half that length again

Total distance = 1 foot + (1/2 × 1)

= 1 + 0.5

= 1.5 feet

A person walked x feet, and then half that length again

Total distance = x + (1/2 × x)

= x + 1/2x

= 1.5x feet

In conclusion, the total distance is calculated by adding the initial distance and additional distance

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In solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.

Multiplication is the opposite of division.

If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

So, the equation is:

4.2p = 29.4

Let's solve as follows:

4.2p = 29.4

p = 29.4/4.2

p = 7

So, the value of p comes to 7.

Where in the image, the value of p is 123.48 which is wrong as the division is not done properly.

Therefore, in solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.

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the answer to the expression 8.3-4 1/5 (6.1+1/2)is -19.42

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The given expression

8.3-4 1/5 (6.1+1/2)

=8.3-4 1/5 (6.6)

=8.3-(6.6*21/5)

=-19.42

Hence the answer is -19.42

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Answer:

reflection over the y-axis

Step-by-step explanation:

Answer:

C?

Step-by-step explanation:

For every prime power pn that divides the order of a finite group G, the Sylow theorems ensure the existence of a subgroup of G of order pn.

What is subgroup?

Sn1 is transitive because normal subgroups of primitive groups are, and as a result, pn1! A transitive group of degree p's centralizer now has order. Given that p is a prime number and n is a positive integer, let G be a finite group of order pn. Assume that H is an index-containing subgroup of G. Note that you can prove it for any boolean interval of rank 4 if you also know the normal subgroups of G. A homomorphism is produced by the left multiplication that G naturally performs on G/H.

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Answer:

The next step is to combine constants

Step-by-step explanation:

1/7 and 3/4 can be written using a common denominator as [tex]\frac{4 + 21}{28}[/tex] or [tex]\frac{4}{28}[/tex] foot and [tex]\frac{21}{28}[/tex] foot.

The term Common denominator is used when the denominator of a number of fractions is a common multiple given fraction.

Step 1

find the LCM of 7 and 4 = 28

Steps 2 and 3

Divide the LCM  of the fractions  = 28, by the denominator given 7 and 4 and Multiply the answer by the numerator.

For  1/7

(28/7) * 1

=4* 1

=4

Thus For  1/7, we have :

4/28

Step 1

find the LCM of 7 and 4 = 28

Step 2 and 3

Divide the LCM  of the fractions  = 28, by the denominator given 7 and 4 and Multiply the answer by the numerator.

For  1/7

(28/7) * 1

=4* 1

=4

Thus For  1/7, we have :

= 4/28

Step 1

find the LCM of 7 and 4 = 28

Steps 2 and 3

Divide the LCM  of the fractions  = 28, by the denominator given 4 and 3 and Multiply the answer by the numerator.

For  3/4

(28/4) * 3

= 7* 3

=21

Thus For   3/4 , we have :

21/28

Hence,1/7 and 3/4 can be written using a common denominator as [tex]\frac{4 + 21}{28}[/tex] or [tex]\frac{4}{28}[/tex] and [tex]\frac{21}{28}[/tex].

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The correct answer is:  [D]:  " [tex]\frac{(1.2)^2^4}{(1.4)^1^8}[/tex]  "

Step-by-step explanation:

Given:  ( 1.4³ / 1.2⁴)⁻⁶ ;

Note the following properties of exponents:

1)    [tex]a^-^b = \frac{1}{a^b}[/tex] ;  { [tex]a\neq 0[/tex] } ;  and:

2)   the  'power of a fraction' rule:
 [tex](\frac{a}{b})^c} =\frac{a^c}{b^c}[/tex] ;  [tex]b\neq 0[/tex] '

As such:
[tex](\frac{1.4^3}{1.2^4})^{-6}[/tex]  ;

=  1  ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;

=  [tex]\frac{1}{1}[/tex]   ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;;

=  [tex]\frac{1}{1}[/tex]   ÷   [tex]\frac{1.4^(^3^*^6^)}{1.2^(^4^*^6^)}[/tex] ;

Note the follow property of exponents:
" [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] " ;  {" b ≠ 0 "}.

⇒ =   [tex]\frac{1}{1}[/tex]   ÷ [tex]\frac{1.4^(^1^8^)}{1.2^(^2^4^)}[/tex]

Note:  Dividing by a fraction or a number; is the same as multiplying by the reciprocal (invert) of that number.

   =   [tex]\frac{1}{1}[/tex]   *  [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] ;

   =     "  [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex]  "  ;

which corresponds to:
Answer choice:  [D]:   " [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] " .
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Hope this is helpful!  Best of luck!

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