The vertex angle of isosceles is triangle ABC is angle C. What can you prove? Select all that apply.
A. AB = BC
B. angle A = angle B
C. angle B = angle C
D. segment BC = segment AC
E. segment AB = segment AC
​

Considering the context of the question and the mathematical expression, the height of the frame. after the width is reduced to 3 inches will be 1.8 inches.

Dimension is a term that is used to describe the measurement of the size or distance of an object or region or space in one direction.

Generally, the term dimension is the measurement of the length, width, and height of anything.

In this case, as given in the question

A frame is 10in wide and 6 in tall.

reduces to a width of 3 in

let us assume that the height of the frame after reducing the width to 3in be = x

then the equation becomes original width/ original length = reduced width/reduced length

put all the value, we get

[tex] = 10 \div 6 = 3 \div x[/tex]

solve the above

[tex]x = (6 \times 3) \div 10 \\ x \: = 1.8in[/tex]

Therefore, in this case, it is concluded that the correct answer is 1.8in, which will be the tall or height of the frame.

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The point (-1, 6) is on the lines y = 5x + 3 and y = 2x + 4​

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

Point = (-1, 6)

Also, we have

y = 5x + 3

y = 2x + 4​

Substitute the known values in the above equation, so, we have the following representation

6 = 5(-1) + 3 = -2 -- false

6 = 2(-1) + 4 = 2 --- false

Hence, the point is not one the line

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The given expression is equivalent to the expression -x² + x + 30.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given expression,
= (5 + x)(6 - x)

Simplifying the expression using distributive property,
= 5 [6 - x] + x [6 - x]
= 30 - 5x + 6x - x²
= -x² + x + 30

Thus, the given expression is equivalent to the expression -x² + x + 30.

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The function that is positive for the entire interval [-3, -2] is given as follows:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0).

A function is positive over an interval if the values of y of the function are above zero for the entire interval.

A function is negative over an interval if the values of y of the function are below zero for the entire interval.

For the function in this problem, we have that:

As the function is concave up, it is positive to the left of the smaller root at x = -1, that is, positive for all x < -1, hence the correct option.

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a) When Ozzie Foster deposits $2,000 at the end of each year,

amount in account after 25 years = $126571.43

b) If Ozzie had deposited the $2,000 at the beginning of each year,

amount in account after 25 years = $135431.43

An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees.

Given,

Value of each payment P = $2000

Rate of interest per period in decimal r = 7% = 0.07 per year

Number of years n = 25

a) future value of ordinary annuity

FV = P×((1+r)ⁿ−1) / r

FV = 2000×((1+0.07)²⁵−1) / 0.07

FV = 2000×((1.07)²⁵−1) / 0.07

FV = 2000×(5.43 - 1 )/ 0.07

FV = 2000×4.43/ 0.07

FV = 8860/0.07

FV = $126571.43

b) future value of annuity due

FV = (1+r)P×((1+r)ⁿ−1) / r

FV = (1+0.07) × $2000((1+0.07)²⁵ - 1)/0.07

FV = 1.07 × 2000×((1.07)²⁵−1) / 0.07

FV = 1.07 × 2000×(5.43 - 1 )/ 0.07

FV = 1.07 × 2000 × 4.43 / 0.07

FV = 2140 × 4.43 / 0.07

FV = 9480.2 / 0.07

FV = $135431.43

Hence,

a) $126571.43 is the amount in the account when Ozzie Foster deposits $2,000 at the end of each year.

b) $135431.43 is the amount in the account If Ozzie had deposited the $2,000 at the beginning of each year.

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Answer:

4,7

Step-by-step explanation:

4,7

Answer:

this statement is true .............

Answer:

There is no mode for this set of numbers.

Step-by-step explanation:

The mode is the value that appears most frequently in a data set.

54,56,60,62,64,67,76,78

In this set of numbers no value appears more than once.

This means there is no mode for this set of data.

Answer:

Step-by-step explanation:

Given the first three terms of the expansion of (1 +x)^n are 1 +3 +4, you want the values of x and n, and the next term.

The first few terms of the binomial expansion of (1 +x)^n are ...

  [tex](1+x)^n=1^n+n\cdot1^{n-1}x+\dfrac{n(n-1)}{2}1^{n-2}x^2+\dfrac{n(n-1)(n-2)}{2\cdot3}1^{n-2}x^3+\dots[/tex]

Comparing the terms to those given, we have ...

  [tex]nx=3\\\\(nx)((n-1)x)/2=4[/tex]

Expanding the second of these equations, and substituting the first, we get ...

  [tex](nx)(nx -x)=8\qquad\text{multiply by 2}\\\\3(3-x)=8\qquad\text{substitute $nx=3$}\\\\9-8=3x\qquad\text{add $3x-8$}\\\\\boxed{x=\dfrac{1}{3}}\qquad\text{divide by 3}\\\\\dfrac{1}{3}n=3\qquad\text{substitute for $x$ in $nx=3$}\\\\\boxed{n=9}\qquad\text{multiply by 3}[/tex]

Then the fourth term is ...

  [tex]\dfrac{n(n-1)(n-2)}{6}x^3=\dfrac{9\cdot8\cdot7}{6}\cdot\left(\dfrac{1}{3}\right)^3=\boxed{\dfrac{28}{9}}[/tex]

__

Additional comment

Then the expansion is ...

  (1 +1/3)^9 = 1 + 3 + 4 + 28/9 + 14/9 + 14/27 + ...

The n-th term is (11-n)/(3(n-1)) times the term before.

The point corresponding to the transformed function y=f(x/x)+1 is approximately (-4, 4.25), (-2, 2.5), (0, 1), (1, -0.5), (3, 1). 

we need to substitute x/x = 1 for the argument of the function f(x) and add 1 to the result.

Transformed point on point y on f(x) = f(x/x) + 1

(x, f(x)) (x, f(x/x) + 1)

(-4, 5) (-4, f(-2) + 1) ≒ (-4, 4.25)

(-2, 3) (-2, f(-1) + 1) ≈ (-2, 2.5)

(0, 0) (0, f(0) + 1)

= (0, 1)

(1, -2) (1, f(1) + 1) ≈ (1, -0.5)

(3, -4) (3, f(3/3) + 1) ≈ (3, 1)

Note that for the point (-4,5) you have to substitute x/x = -1/2 instead of x/x = 2. This gives x = -8. So the corresponding transformed point is (-4, f(-8) + 1) ≈ (-4, 2.75).

So the point corresponding to the transformed function y=f(x/x)+1 is approximately

(-4, 4.25), (-2, 2.5), (0, 1), (1, -0.5), (3, 1). 

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Check the picture below.

Answer:

x = 4

Step-by-step explanation:

We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)

Big triangle:little triangle

25:5

5:1

So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.

Solve for x:

3x+8 = 4(5) [ratio!!]

3x+8 = 20

(subtract 8 from both sides)

3x = 12

(divide both sides by 3)

x = 4

Thus, we have our answer!

The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x + y + z) / (4xy²)

The expression if x = -3, y = 5, and z = 2. Then the value of the expression is given as,

⇒ (-3 + 5 + 2) / (4 × (-2) × (2)²)

⇒ - 4 / 32

⇒ - 1 / 8

The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.

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Answer:

Step-by-step explanation:

Answer: To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The theorem is written as c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

In this problem, we are given that the lengths of the legs of the right triangle are 7 inches and 2 inches. We can substitute these values into the Pythagorean theorem and solve for c, the length of the hypotenuse.

So, we have c² = 7² + 2².

So, c² = 49 + 4

So, c² = 53

Now, we can take the square root of both sides of the equation, since c² = 53, we can say c = √53

To round to the nearest tenth, we look at the digit in the thousandths place (the 3rd digit after the decimal point). Since 3 is greater than or equal to 5, we round up, so c = 7.28, so the hypotenuse is 7.28 inches.

Step-by-step explanation:

Answer:10

Step-by-step explanation: round it together and you get 10

The domain and range are (0 , ∞) and (0 , ∞).

What is domain ?

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The set of all initial elements in ordered pairs constitutes the domain (x-coordinates). The set of all second items in ordered pairs is the range (y-coordinates).

Given

y = 80 / x

As per the graph the domain and range are

domain : (0 , ∞)

{depth of the diamond > 0 }

range : (0 , ∞)

{ratio > 0}

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Answer:

a) General Equation for this scenario is

[tex]\boxed{P_n = P(.98)^n\\\\}[/tex]

where P is the starting population and Pₙ is the population at the end of n years

For this specific case,
[tex]\boxed{P_n = 20000(0.98)^n}[/tex]

b) Population in 2025 will be the population after 25 years:
[tex]P_{25} = 20000(0.98)^{25} = \boxed{12,069}[/tex]

Step-by-step explanation:

In general, if the population at year 0 is P and it decreases by 2% each year then the population after one year will be given by

P - decrease in one year

Decrease in population for 1 year = 2% of P [tex]= 0.02P[/tex]

So P(after 1 year) :  
[tex]P - 0.02P\\\\ = P(1-0.02) \\\\= 0.98P[/tex]

After 2 years the population will be population after 1 year (0.98P) - decrease in population for 1 year (0.02 x 0.98P)

So population at end of 2 years would be
 [tex]0.98P - 0.98P(0.02)\\\\= 0.98P(1-0.02)\\\\=0.98P(0.98)\\\\= P(0.98)^2[/tex]

In general after n years the population would be
[tex]P(0.98)^n\\\\[/tex]

If the population in year 2000 is 20,000 then population at the end of 25 years is:

[tex]20000(0.98)^{25}[/tex]
[tex]\rm\:{=\:12,069\:\;\:rounded\:down\:to\:the\:nearest\:integer}[/tex]  

Answer:

-34 - 24i

Step-by-step explanation:

To calculate ( – 2 – 3i)^4, we can use the property that (a + bi)^n = a^n + (n*a^(n-1)b)i + (na^(n-2)*b^2)i^2 + ...

So, ( – 2 – 3i)^4 = (-2 - 3i) * (-2 - 3i) * (-2 - 3i) * (-2 - 3i)

= -2^4 - 2^3 * 3i - 2^2 * 3^2i^2 - 2 * 3^3i^3 - 3^4i^4

= -16 - 24i + 18i^2

= -16 - 24i -18

= -34 - 24i

Answer:

Question 4:

Question 5:

Question 6:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the line x = -1, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 180° about the origin, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 270° about the origin, the transformation rule is:

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are:

The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) To find the maximum score that can be in the bottom 5% of scores, we need to find the score that corresponds to the 5th percentile of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28. To convert this back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

To find the range of scores that the middle 90% of scores lie between, we need to find the 5th and 95th percentiles of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28 and the 95th percentile corresponds to a standard normal score of 1.28. To convert these back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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Answer:

19.7

Step-by-step explanation:

A^2 + B^2 = C^2

8^2 + 18^2 = sqrt(388)

Answer:

Step-by-step explanation:

Assuming that there are no sidewalks or other obstructions, the estimated size of the crowd along a 3-mile section of the parade route would be approximately 3,780,400 people. This calculation is based on the assumption that people will be standing shoulder to shoulder and that each person will take up an area of 5 feet by 11 feet. This would mean that for each mile of the parade route, there would be 1,260,800 people standing (12 people x 10 feet x 5280 feet). Multiplying this by 3 gives us 3,780,400 people.

Answer:

12 people fitting in an area of 5*5 = 25 ft². Area of the street: 3 miles = 3*5280 ft = 15840 ft 25 feet on both sides. So, the total area in which the crowd is sparsed is: A = 15840*25*2= 792000 ft². Now we apply the ratio: People over area. Applying cross multiplication: 25x = 12*792000 x = (12*792000)/25 x = 380160

Step-by-step explanation:

Answer:all integers

Step-by-step explanation:

the correct is all integers

Answer:

Step-by-step explanation:

Is there enough evidence to reject the researcher claim?

To determine if there is enough evidence to reject the researcher's claim, we can perform a hypothesis test with a null hypothesis of p <= 0.05 (at most 5% of working college students are employed as teachers or teaching assistants) and an alternative hypothesis of p > 0.05 (more than 5% of working college students are employed as teachers or teaching assistants).

Find the critical values and identify the rejection.

For a one-tailed test with a significance level of alpha = 0.05, the critical value for a z-test would be 1.645. This means that if the calculated z-score is greater than 1.645, we would reject the null hypothesis.

Find the standardized test statistic z

To find the standardized test statistic z, we can use the formula:

z = (p-hat - p0) / (sqrt(p0 * (1 - p0) / n))

where p-hat is the sample proportion of working college students employed as teachers or teaching assistants (6%), p0 is the proportion specified in the null hypothesis (5%), and n is the sample size (400).

z = (0.06 - 0.05) / sqrt(0.05 * (1 - 0.05) / 400)

z = 0.1 / 0.015811388300841898

z = 6.317

Decide whether to reject or fail to reject the null hypothesis and interpret the decision.

Since the calculated z-score (6.317) is greater than the critical value (1.645), we can reject the null hypothesis. This means that there is enough evidence

Answer: 8.8 hours

Step-by-step explanation:

To start off, we’ll make an equation that “connects” both companies:

10 + 4.75h = 21 + 3.5h (we put h to represent the number of hours)

Move all similar terms to one side:

4.75h - 3.5h = 21 - 10

Simplify:

1.25h = 11

h = 8.8

I hope this helps!

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

y = - [tex]\frac{1}{2}[/tex] x + 6 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

slope of parallel line = - [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of parallel line

The amount of mulch that he put on each vegetable bed will be 1/9.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this situation, the gardener spread 1/3 of a bag of mulch evenly over his 3 equal-sized vegetable beds.

The amount of mulch that he put on each vegetable bed will be:

= 1/3 ÷ 3

= 1/3 × 1/3

= 1/9

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The total number of marbles are 30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, to start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.

Here, m/3 =10

m=30

Therefore, the total number of marbles are 30.

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