Peter and Vivian each wrote a proof for the statement: if , then is supplementary to . A supplementary angle line with angles of 1 and 2. Another obtuse angle with the angle of 3 Peter's proof: By the linear pair theorem, is supplementary to . So, . Since , then . Applying the transitive property of equality, , which means is supplementary to . Vivian's proof: Suppose is not supplementary to . So, . By the linear pair theorem, is supplementary to . By the definition of supplementary angles, . Applying the Transitive Property, . By the subtraction property of equality, this implies that . By definition of congruence, . However, contradicts the given. What type of proofs did they use? Peter used because . Vivian used because . Reset Next

The value of the angle x is 110 degrees

A transversal is described as a line that passes two lines of distinct points

Also, we need to know that pair of angles on a straight line sums up to 180 degrees.

Supplementary angles are described as angles that sum up to 180 degrees.

Corresponding angles are also equal, then, we have that;

70 + x = 180

collect the like terms, we get;

x = 180 - 70

subtract the values, we have;

x = 110 degrees

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Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

The rate of the speeding car is 0.493.

We have,

The police car is at 80 mph and it is 44 yards from the intersection, is increasing at 45 mph, while the other car is 117 yards away from the intersection.

So, Rate of speeding car

= (45- 80)/ (117- 44)

= -35/(-73)

= 35/73

= 0.493

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Answer:

Kari = 20 hours

Chris = 10

Mark = 10

Explanation:

K is Kari's hours

C is Chris's hours

Karis = 2 x C = K

Chris = C

Mark = C

3C - 10 = K

Assume C is 10 (since 10 is 1/3 of the hours mentioned)

2 x 10 = 20 so K worked 20 hours

20 is twice as much as 10 (C's hours)

and it's 30 - 10 (10 less than 3 times as many hours as Mark)

35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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The prοbability that exactly 13 οf the 20 pitches are strikes is apprοximately 0.1835 οr 18.35%.

The binοmial distributiοn is a prοbability distributiοn that mοdels the number οf successes in a fixed number οf independent trials with a cοnstant prοbability οf success.

It is used tο calculate the prοbability οf getting k successes in n trials, where each trial has a prοbability οf p οf success.

The fοrmula fοr the prοbability οf k successes in n trials with prοbability p οf success in each trial is:

               \(P(k) = (n, k) \times p^{k} \times (1-p)^{n-k}\)

Here we have

A softball pitcher has a 0.64 probability of throwing a strike for each pitch. The softball pitcher throws 20 pitches,

This problem can be solved using the binomial distribution

The formula for the probability of k successes in n trials with probability p of success in each trial is:

    \(P(k) = (n, k) \times p^{k} \times (1-p)^{n-k}\)

On substituting the values, we get:

P(13) = (20, 13) × 0.64¹³ ×(1-0.64)⁽²⁰⁻¹³⁾

= (20! / (13! × 7!)) × 0.64¹³ × 0.36⁷

= 77520 × 0.00000236

= 0.1835 (rounded to four decimal places)

Therefore,

The probability that exactly 13 of the 20 pitches are strikes is approximately 0.1835 or 18.35%.

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Answer:

cs.a,C|"< dl\vds

Step-by-step explanation:

Answer:

Pang, Ruben, Adela, Tony

Step-by-step explanation:

So the Answer would be c. I hope this helped and have a good day.

Answer:

c

Step-by-step explanation:

Answer: Yes

Step-by-step explanation: They are similar because it the same kind of triangle just ones smaller and the other is bigger.

Answer:

Need Decimal-

Step-by-step explanation:

The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.

Function

The function is referred as a mathematical expression that defines a relationship between one variable and another variable.

Given,

Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.

Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.

Here the x = 3 is a vertical asymptote.  

So the one factor in the denominator is (x - 3),

And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.

Therefore, the rational function would be :

f(x)  = (x + 2)/(x - 3)(x + 2)

So, the rational function would be (x + 2)/(x - 3)(x + 2).

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Answer:

16.11 (appx.)

Step-by-step explanation:

since l and m are parallel and a line intersects them, so we can say that the line is the transversal. from the figure we see that

7x + 12 = 12x - 28 [they are internal alternate angles and alternate angles are always equal to one another]

now, we can find the value of x from the equation

12x - 7x = 28 + 12

⇒ 5x = 40

⇒ x = 8

so the angle (7x+12)° is ((7*8)+12) = 68°

so (12x-28)° is also equal to 68° [cause of being alternate angles]

now, look at the figure,

angle (9y-77)° & (12x-28)° add upto a straight line as in 180°

and we know (12x-28)° = 68°

so now,

9y-77 = 68

⇒9y = 68+77

⇒9y = 145

⇒y = 16.11 (appx.)

Given:

To solve, we can use a table of values:

Y valueX value

16-3

9-2

4-1

10

01

12

As we can see from the table, f(x) =0 when x =1.

Thus x = 1 is a solution to our equation.

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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Answer:

C - 403

Step-by-step explanation:

Answer:

See Picture. I made a 100.

Step-by-step explanation:

Weekly- $17253.46

Daily- $17254.01

Continuously- $17254.11

Monthly- $17251.29

Semi-annually- $17237.36

Quarterly- $17245.69

Compound interest is the addition of interest on the interest of the principal amount.

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

\(A = P(1+ \dfrac{r}{n})^{nt}\)

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46\)

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55\)

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

\(A = Pe^{rt}\)

Substitute the values, we will get,

\(A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45\)

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23\)

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36\)

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7\)

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Answer: We can set up the following pair of simultaneous equations:

a + c = 6.70 (equation 1) (the total amount of money they have is ₹6.70)

a = c + 1.70 (equation 2) (Alan has ₹1.70 more than Conner)

We can substitute equation 2 into equation 1 to eliminate a:

(c + 1.70) + c = 6.70

Simplifying and solving for c:

2c + 1.70 = 6.70

2c = 5.00

c = 2.50

So Connor has ₹2.50.

We can substitute this value into equation 2 to find the value of a:

a = c + 1.70

a = 2.50 + 1.70

a = 4.20

Therefore, Alan has ₹4.20.

Answer:

-6g + 7h

Step-by-step explanation:

Answer:

\(b.)= (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)

Step-by-step explanation:

Given;

velocity of the diver, v = 25 mph

direction of his dive, θ = 60°

The vertical component of the velocity is given by;

\(-V_y = vsin\theta \ \ (below \ horizontal \ is \ in \ negative\ y-direction)\\\\V_y =-(25)(sin 60)\\\\V_y =-(25)(\frac{\sqrt{3} }{2} )\)

The horizontal component of the velocity is given by;

\(V_x =vcos\theta\\\\V_x =(25)(cos 60 )\\\\V_x =(25)(\frac{1 }{2} )\\\\V_x = \frac{25}{2}\)

Therefore, the component form of the velocity vector is given by;

\((V_x, \ V_y) = (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)

correct option = \(b.)= (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)

Answer:

B: (25/2, - 25√3/2)

Step-by-step explanation:

First find the values

v = 25 mph

θ = 60°

Vertical:

\(V_{y}\) = -vsin(θ) (Negative because it is below the x axis.)

\(V_{y}\) = (-25)(sin(60))

\(V_{x}\) = (-25)(\(\frac{\sqrt{3} }{2}\))

\(V_{y}\) = \(\frac{-25\sqrt{3} }{2}\)

Horizontal:

\(V_{x}\) = vcos(θ)

\(V_{x}\) = (25)(cos(60))

\(V_{x}\) = (25)(1/2)

\(V_{x}\) = \(\frac{25}{2}\)

Putting them together we get:

(\(\frac{25}{2}\), \(\frac{-25\sqrt{3} }{2}\)) or B

ANSWER

(x + 15)(x - 15)

EXPLANATION

The difference of squares is equivalent to the product of the sum and subtraction of the bases,

So, to factor this difference of squares, we have to find the principal square roots of each term,

So this is,

Hence, the factored form is (x + 15)(x - 15).

The standard deviation is 4.0, while mean is 10.2.

Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Mean = 10.2

The standard deviation is 4.0.

Age in the mean is the average age.

Mean = (16 + 10 + 5 + 7 + 13)/5

Mean = 51/5 = 10.2

The variance's square root will reveal the standard deviation.

(16 - 10.2) + (10 -10.2) + (5-10.2) + (7-10.2)+( 13-10.2) ( 13-10.2)

5.8 + 0.2 -5.2 - 3.2 + 2.8

each number into squares

33.64 + 0.04 + 27.04 + 10.24 + 7.84

Variation: 78.8/5 = 15.76

Standard deviation = 3.969 = 4.0.

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The complete question is,

16, 10, 5, 7, 13

What is the porcupines' typical age based on your sample? Where can I find the standard deviation? in a circle tenths of a percent, closest.

Answer:

Step-by-step explanation:

put all of the sets in a mean median and mode calcultor then add the three numbers toghter

Answer:

90.393

Step-by-step explanation:

Answer:

"90.393"

Step-by-step explanation:

quoted from "https://percentages.calculators.ro/22-number-increased-with-percentage-of-its-value.php?number=87&percentage_increase=3.9&new_value=90.393"

The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

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Answer:

The correct answers are A and E

Step-by-step explanation:

Answer:

The length of the third side is 3x

Step-by-step explanation:

Algebraic Expressions

This problem deals with the ability to manage algebraic expressions in two variables.

Recall the perimeter of a triangle is the sum of its three sides. We already know the perimeter of the triangle is:

P=13x+5y

We also know the lengths of two of its sides are 2x+y and 8x+4y. The sum of those sides is:

S2=2x+y+8x+4y

Joining like terms:

S2=10x+5y

The third side must be the difference between the perimeter and the sum above:

S3=13x+5y-(10x+5y)

Operating:

S3=13x+5y-10x-5y

Joining like terms:

S3=3x

The length of the third side is 3x