Norma and Vincent, the boy she was babysitting, were playing basketball together. Her score was 19 points, and his score was 17 points. Norma wanted to make the game more fair, so she called a time-out and modified the rules a bit. Norma explained that, for the rest of the game, she would get 2 points per basket, and Vincent would get 3 points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many points did each person have at the end? How many baskets did each person make after the time out?


Norma and Vincent each scored __by making ___baskets after the time-out.

The probability that the mean weight of the sample is less than 6.15 ounces as per the given data is 0.1806.

Mean, μ = 6.16 ounces

Standard Deviation, σ = 0.13 ounce

Sample size, n = 38

We are informed that the weight of the cans is distributed in a bell-shaped manner, which is a normal distribution.

Formula:

Z-score = ( x - ц) /standard deviation

Standard error due to sampling

=SD/√n

=0.13/ √(38)

=0.021

P(weight of the sample is less than 6.15 ounces)

P(X < 6.15) =P( Z< (6.15 - 6.16)/0.021 )

= P(Z> -0.476)

=0.1806 ( as per the Z- score table)

The probability that the sample's mean weight is less than 6.15 ounces is 0.1806.

To learn more about probability

https://brainly.com/question/13016713

#SPJ4

The minimum amount of tournaments Amanda and Jennifer each need to play in order to have played the 40 number of games are 4 and 5 respectively.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given that Amanda is playing has 10 games and the tennis tournament that Jennifer is playing has 8 games.

Now we will find the minimum same number of games in tournaments,

for that we will find the LCM of the numbers.

LCM of Amanda games in tournament and Jennifer games in tournament.

LCM of 10 and 8 is 40.

Therefore, the minimum amount of tournaments Amanda and Jennifer each need to play in order to have played the 40 number of games are 4 and 5 respectively.

To learn more about the LCM;

https://brainly.com/question/20739723

#SPJ1

The edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. Hence, the rate of change of the volume of the cube at that instant will be 2178  [tex]inches^3[/tex] /s.

The volume of the cube V = [tex]a ^ 3[/tex]

where 'a' is the edge.

Rate of increase of volume = dV / dt = 3a^2 da/dt.

da/dt = 6 inches /s

dV / dt = 3 [tex]a^2[/tex] da/dt.

When a = 11 inches.

dV /dt = 3 x [tex]11 ^2[/tex] x 6

           = 3 x 121 x 6

           = 2178  [tex]inches^3[/tex] /s

Hence, the rate of change of the volume of the cube at that instant will be 2178  [tex]inches^3[/tex] /s.

Read more about the Volume of the cube:

brainly.com/question/21549952

#SPJ4

The amount of fencing feet the city needs to enclose the pond is 94.29 feet.

Perimeter can be defined the total distance around an object.

To calculate the amount of fencing the city needs to enclose the pond, we use the formula for the perimeter of a circle.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the feet of fencing needed is 94.29 feet.

Learn more about perimeter here: https://brainly.com/question/25092270

#SPJ1

Answer:

  C.  Yes, SAS

Step-by-step explanation:

You want to know the congruence theorem that lets you say ∆ACD≅∆CAB, given that AB=CD and AB║CD.

The triangles are congruent if an angle or side can be shown congruent, in addition to at least one angle and at least one side.

Here, the sides AB and CD are shown congruent. The side AC is congruent to itself, so we only need the angle(s) between them to show the triangles are congruent.

The Alternate Interior Angles theorem tells you that transversal AC creates congruent angles CAB and ACD with respect to the parallel lines AB and CD.

Hence we can show triangle ACD and CAB are congruent by the SAS congruence theorem.

Yes, The triangle is congruent by Angle - Side - Angle  congruence theorem.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB || CD

Now,

In figure,

⇒ AB || CD

So, In triangle ACD and triangle CAB;

⇒ AB || CD

So, By definition of alternate angles,

⇒ ∠ BAC = ∠ DCA

And, ∠ DAC = ∠ ACB

Here, Line AC is common in both tringle.

Hence, By Angle - Side - Angle  congruence theorem,

⇒ Δ ACD ≅ Δ CAB

Thus, The triangle is congruent by Angle - Side - Angle  congruence theorem.

Learn more about the triangle visit:

https://brainly.com/question/13984402

#SPJ1

Answer:

For every 1 box Naveah moves, Michael moves 4 boxes

The snow level at 8 a.m., when x = 8, was 30cm.

The simplest equation for expressing and resolving an unknown number is a linear equation in one variable. It is usually a straight line and is easily pictorial portrayed. A simple way to convey a mathematical assertion is with a linear equation. Unknown numbers can be represented by any variable or symbol. There are several easy ways to solve a linear equation.

y = 2x + 14.

Here, y is the amount of snow in inches, and x is the number of hours after midnight

To find the snow level at 8 a.m. we take the value of x = 8.

⇒ y = 2*8 + 14

⇒ y = 16 + 14

⇒ y = 30cm

So, The snow level at 8 a.m., when x = 8, was 30cm.

To learn more about linear equation visit:

brainly.com/question/21835898

#SPJ1

this question is incomplete. The complete question is

the snow level is modeled by the function y = 2x + 14. Here, y is the amount of snow in inches, and x is the number of hours after midnight (x = 0). 10. What was the snow level at 8 a.m., when x = 8?

Answer:

A) They have the same y intercept and the same rate of change

Step-by-step explanation:

Write the equation for the line passing through the points (2,4) and (12,7)

Slope [tex]\frac{7-4}{12-2}[/tex] = [tex]\frac{3}{10}[/tex] = .3

y intercept  (b)

y = mx + b

Use 2 fox x, 4 for y and .3 for m

y=mx + b

4 = .3(2) + b

4 = .6 + b    Subtract .6 from both sides

3.4 = b

The equation is

y = .3x + 3.4

The two equation are identical so the slope and y intercepts are the same.

compare the y-intercept and the rate of change of the following items. Option (d) The rates of change are the same, but the y-intercepts are different. is correct.

for rates,

we will find the slope of I and II

slope = dy/dx = change in y/change in x

for both of them when we compare the slope, it is 0.3.

for y-intercepts.

equation for II should be formed in order to compare with the y-intercept of I which is  3.4.

y-7=0.3(x-12) .................(i)

so, the y-intercept is 7 for II

thus, the y-intercepts of given eq are not equal.

Answer:

The answer is 2

Step-by-step explanation:

5x + 7y = -11

y = -3

Now, put the value of y in the given equation we get,

5x + 7y = -11

5x + 7(-3) = -11

5x - 21 = -11

5x - 21 + 21 = 21 - 11

5x = 10

5x/5 = 10/5

x = 2

Thus, The value of x is 2

By using percentage, it can be calculated that

2% of the product of 19 and the average of 63,500, 65,000 and 66,500 = 24700

What is percentage?

Suppose, there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example, 7% means [tex]\frac{7}{100}[/tex]. Here, 7 is expressed as a percentage of 100.

This is a problem on percentage

The numbers are 63,500, 65,000 and 66,500

Average = [tex]\frac{63500 + 65000 + 66500}{3}[/tex] = 65000

Product of 19 and 65000 = 65000 [tex]\times[/tex] 19 = 1235000

2% of 1235000 = [tex]\frac{2}{100} \times 1235000[/tex] = 24700

To learn more about percentage, refer to the link-

https://brainly.com/question/24304697

#SPJ1

There are Three months in a quarter of a year.

To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:

1 year = 4 quarters

1 quarter= [tex]\frac{1}{4}[/tex] year

1 year = 12 months

Thus,

1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)

1 quarter = [tex]\frac{12}{4}=3[/tex]

So, There are Three months in a quarter of a year.

One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).

To learn more about fiscal year, visit:

brainly.com/question/15875620

#SPJ4

There are Three months in a quarter of a year.

To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:

1 year = 4 quarters

1 quarter= [tex]\frac{1}{4}[/tex] year

1 year = 12 months

Thus,

1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)

1 quarter = [tex]\frac{12}{4} =3[/tex]

So, There are Three months in a quarter of a year.

One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).

To learn more about fiscal year, visit:

brainly.com/question/15875620

#SPJ4

Proof of  angle 6 is congruent to angle 4 is given.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Angles of equal measure are said to have congruent angles.

Given,

∠1 ≅ ∠3

And we know from the vertical angles, property;

The angles opposite each other when two lines cross.

They are always equal.

And here we have two pairs of vertical angles,

So, ∠1 = ∠4

and ∠3 = ∠6

And ∠1 ≅ ∠3 is given.

So,  ∠1 ≅ ∠4

and ∠3 ≅ ∠6

Comparing, we get

∠4 ≅ ∠6

Therefore, ∠4 ≅ ∠6 is proved.

To learn more about the congruent;

https://brainly.com/question/12413243

#SPJ1

Answer:

0.0084033613

Step-by-step explanation:

The length of g 1029.8 in the given  ΔFGH.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The Law of Sines (or Sine Rule) is very useful for solving triangles:

[tex]\frac{a}{sinA} = \frac{b}{sinB} + \frac{c}{sinC}[/tex]

840 / sin(38) = g /sin(49)

g = (840 / sin(38) ) *sin(49)

g= (840/0.615) *0.754 = 1029.8

Hence, the length of g 1029.8 in the given  ΔFGH.

Learn more about Trigonometric Functions, by the following link.
https://brainly.com/question/1143565
#SPJ1

Answer:

The answer is 77.5

Step-by-step explanation:

If light travels 31 times around the Earth in 4 seconds then in 8 seconds it would be 62 times and 15.5 is half of 31 and then we add 15.5 to 62 and we get 77.5. Hope this helps!

Answer:

In 4 seconds light can travel = 31 times

Then in 10 second it can travel=

31/4 ×10 =77.5times

The inequality - 2 · x + y > - 4 represents the figure on Cartesian plane.

In this problem we have a picture with a representation of a linear inequality of the form:

y > m · x + b

Where:

By analytic geometry, a line can be generated from the knowledge of the location of two points on Cartesian plane. First, determine the equation of the line:

m · 0 + b = - 4

2 · m + b = 0

b = - 4

2 · m = - b

m = - b / 2

m = 2

Second, write the inequality:

y > 2 · x - 4

- 2 · x + y > - 4

To learn more on inequalities: https://brainly.com/question/20383699

#SPJ1

The percent of increase in yearly sales is 35%.

A percentage increase means the eventual increase in the quantity in percent form. The percentage increase formula is use to compare growth in a quantity from the initial value to its final value over a period of time.

The formula for getting a percentage increase is "[(Final Value - Initial Value)/Initial Value] × 100"

Initial value = 720,460 pictures

Final value = 972,621 pictures.

The percentage increase:

= [(972,621 - 720,460] / 720,460} * 100

= 0.35 * 100

= 35%

Read more about percentage increase

brainly.com/question/28398580

#SPJ1

The value of x is x ≤ 9 for which y ≤ -5(x - 18) - 2 when y = 43.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is y ≤ -5(x - 18) - 2.

Now the values of x when y = 43 is,

43 ≤ - 5(x - 18) - 2.

43 ≤ - 5x + 90 - 2.

43 - 88 ≤ - 5x.

- 45 ≤ - 5x.

5x ≤ 45.

x ≤ 9.

learn more about inequalities here :

https://brainly.com/question/11612965

#SPJ1

Answer:

Step-by-step explanation:

Are you after a solution for y?

quotient of y and 3 is a fancy word for division

y/3+9=10

To solve for y subtract 9 from both sides

y/3+9-9=10-9

y/3=1

To solve for y

multiply both sides by 3

3(y/3)=1*3

y=3

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.

To learn more about complementary angle, click on below link:

https://brainly.com/question/17887450

#SPJ1

Answer:

B. ​No, the congruent angles are not the included angles.

Step-by-step explanation:

The SAS (Side-Angle-Side) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

In the given figure, we can see that two sides of the two triangles are congruent: side AB is congruent to side DE, and side AC is congruent to side DF. However, the included angles, which are the angles formed by these sides, are not congruent. Angle BAC is not congruent to angle EDF.

Since the included angles are not congruent, we cannot use the SAS Postulate to conclude that the two triangles are congruent. Therefore, the correct answer is B: No, the congruent angles are not the included angles.

Answer:

  B.  ​No, the congruent angles are not the included angles.

Step-by-step explanation:

You want to know if the triangles shown are congruent by SAS.

The SAS congruence postulate tells you that two triangles are congruent if the angles between corresponding congruent sides are congruent. (The A=angle is between the S=side in SAS.)

In the diagrams, the marked angles are not between the marked sides. The SAS postulate cannot be used with these triangles.

In short, ...

  No, the congruent angles are not the included angles

<95141404393>

The function simulates exponential decay, and it degrades by 5.1% for every increment in x.

Explosive increase and decay are common in situations where quantities change rapidly. It has been suggested that exponential development and decay follow a geometric progression. Quantities that change exponentially rather than continually are referred to be exponentially growing or decaying.

As per the given data in the question,

An exponential function with the formula y = a[tex]r^x[/tex] is the function that is given.

a = 330

r = 0.949

The function indicates exponential growth if the base r is larger than 1. The function shows exponential decline if indeed the base r is far less than 1. In this instance, the function depicts exponential decline because the base r is smaller than 1, or 0.949.

If we want to describe the rate of reduction as a percentage, we can remove the base r by 1 and multiply it by 100.

The rate of reduction as a percentage in this instance is:

1 - 0.949 = 0.051 ×100

= 5.1%.

To know more about exponential decay:

brainly.com/question/15352175

#SPJ1

Answer:

  $808.76

Step-by-step explanation:

You want the simple interest earned on $1975 at the rate of 9.1% per year for 4.5 years.

The amount of simple interest is given by the formula ...

  I = Prt

where principal P is invested at rate r for t years.

Using the given values, the amount of interest earned is ...

  I = $1975·0.091·4.5 = 808.7625 ≈ $808.76

The amount of simple interest is $808.76.

<95141404393>

The value of the one-gram quantity in ounces will be 0,35274 ounces.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quantity of some materials is measured in 10 grams. The quantity of the material in ounces will be calculated as,

1 grams = 0.035274

10 grams = 10 x 0.035274

10 grams = 0.35274 ounces

Therefore, the value of the one-gram quantity in ounces will be 0,35274 ounces.

To know more about unit conversion follow

https://brainly.com/question/141163

#SPJ1

George Canter showed that, for any set a, we have |a|<|p(a)|. This is a well-known theorem of canter, known as the 'Canter's Theorem'.

Proving this theorem:                                              

Proof: At the first instance, we need to show that, A bar ≤P(A) bar, we will define the injection by  f:A→P(A) by: f(a)={a}. Let g be the contradiction.

We need to prove that there is no bijection  g:A→P(A).

Now, Let: S={a∈A:a∉g(a)}⊆A.}

In the present condition, there are two possibilities,  first, x∈S  and second, x∉S.

Therefore,

1. If x∈S, then x∉g(x)=S, i.e., x∉S, a contradiction.

2. If x∉S, then x∈g(x)=S, i.e., x∈S, a contradiction.

Thus, such a bijection, is not possible.

This theorem, coined by Canter, basically implies that there is no largest cardinal number present. There are 'n' number of cardinal numbers present, i.e., there are infinite number of cardinal numbers.

Now, suppose that, A is a set of all sets, this was proved by the continuum hypothesis.  But, the continuum hypothesis can't be proved. It can't be disproved also.

To know more about the Cantor's Theorem:

https://brainly.com/question/29516991

#SPJ4

To test the claim that meal preference and gender are not related, you can use a chi-squared test for independence.

The null hypothesis for this test is that there is no relationship between the variables, while the alternative hypothesis is that there is a relationship. To conduct the test, you will need to calculate the chi-squared statistic and compare it to the critical value from a chi-squared distribution with one degree of freedom. The degrees of freedom for this test are calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2-1)*(2-1) = 1.

To calculate the chi-squared statistic, you will need to compare the observed frequencies in the table to the expected frequencies if the null hypothesis were true. The expected frequency for each cell is calculated as the row total * column total / sample size.

For example, the expected frequency for females who prefer hamburgers is (39 * 15)/59 = 12.71. The chi-squared statistic is then calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. In this case, the chi-squared statistic would be:

((15-12.71)^2/12.71) + ((23-26.29)^2/26.29) + ((24-26.29)^2/26.29) + ((16-12.71)^2/12.71) = 7.39

To determine whether this result is statistically significant, you would compare the chi-squared statistic to the critical value from a chi-squared distribution with one degree of freedom. At a significance level of 0.05, the critical value is 3.84. Since the chi-squared statistic (7.39) is greater than the critical value (3.84), you can reject the null hypothesis and conclude that there is a relationship between meal preference and gender in this sample.

Learn more about chi-squared statistic at:

brainly.com/question/4543358

#SPJ4

Answer:

y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{5}{4}[/tex] x - 1 ← is in slope- intercept form

with slope m = [tex]\frac{5}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex] , then

y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (4, 5 ) into the partial equation

5 = - [tex]\frac{16}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{16}{5}[/tex] = [tex]\frac{25}{5}[/tex] + [tex]\frac{16}{5}[/tex] = [tex]\frac{41}{5}[/tex]

y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex] ← equation of perpendicular line

Answer:

6 7/12

Step-by-step explanation:

"12 1/4 - 5 2/3" is an expression.  It is not said to equal anything.  The "=" sign makes it an equation.  But we can evalute an expression by simplyfying it.  Let's do the subtraction.  We first need to convert one of the fractions so that it has the same denominator as the other.

12 1/4 - 5 2/3 can be written as (12 - 5)+(1/4 - 2/3)

(12 - 5)+(1/4 - 2/3)

(7)+(1/4 - 2/3)        Let's convert both fractions to have denominators of 12 [since 4*3 = 12]

7 + 1/4 - 2/3

7 + (1/4)*(3/3) - (2/3)*(4/4)   [Multiply the tqo fractions by (3/3) and (4/4), repectively.  This is OK since both are the equivalent of multiply by 1.  But it converts the denominators so that we can now add or subtract.

7 + (3/12) - (8/12)

7 - (5/12)

or 6 7/12