Examine the triangles below, how do we know the triangles are congruent?

Please help it if for a test worth 105 points

For x = 1000 cell phones, the average cost per cell phone will be $150.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

To solve for x, we can rearrange the equation to solve for x:

y = 30000 + 120x/x

Isolating x on one side of the equation gives:

x = 30000/(y - 120)

Substituting y = 150 into this equation gives:

x = 30000/(150 - 120)

This simplifies to:

x = 30000/30

Which simplifies to:

x = 1000

Hence, for x = 1000 cell phones, the average cost per cell phone will be $150.

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The equations that represent given problem is

P + S = 384 and 2.50P + 1.25S = 696.25.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given that the cost of 1 slice pizza is $2.50.

The cost of 1 bottle can of soda is $1.25.

In total sell for a day is 384.

Assume that you sell P slice of pizza and S number of soda bottle.

Thus your total sell is P + S.

Therefore, P + S = 384.

The cost 1 slice pizza is $2.50

Then the cost P slice of pizza is $2.50P.

The unit rate of soda bottle is  $1.25.

Then the cost S bottles of soda is $1.25S.

Therefore the total sell for that day is 2.50P + 1.25S

2.50P + 1.25S = 696.25

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Answer: i think 15/8 but, im not sure

Step-by-step explanation:

An expression which describe the given sequence is, an = -2 + n.

Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.

an = -2 + n is an expression which describe the given sequence

The general rule for the arithmetic sequence is given by,

 an = a + (n - 1)d  ......[1]

where, denotes the initial word.

the common difference

there are n terms;

The given order is -1, 0, 1, 2,.....

This is a frequent difference arithmetic sequence.

Since,0-(-1) = 1

1-0 =1

2-1 = 1 ....

Here, a1 = -1

When you replace [1] with the value of d = 1, you get, a1 = -1

an = -1 + (n -1)(1)

an = -2 + n

Consequently, the following expression describes the given sequence: an = -2+n.

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As per the binomial distribution, the value of the normal approximation is 0.6573

The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

Here we have given that n = 95 P = 0.96 and q = 0.04

Now, here we have to check  the binomial distribution to see whether it can be approximated by the normal distribution.

While we looking into the given question we know that the value of n = 95 P = 0.96.

Then as per the binomial distribution formula, the normal distribution is calculated as,

=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴

When we simplify this one then we get the value as 0.6573

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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Answer:

p = 72

Step-by-step explanation:

If we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.

4 × y =?

5 × y =?
We need to put a value in for y.

Let's use 9.

4 × 9 = 36 (P)

5 × 9 = 45 (Q)

Now let's add 12 to P, and take away 6 from Q.

36 + 12 = 48

45 - 6 = 39

The numbers aren't the same yet.

Let's use a different value for y.

y = 18

The equations will now look like this:

4 × 18 = 72 (P)

5 × 18 = 90 (Q)

Let's add 12 and 6 to the numbers again.

72 + 12 = 84

90 - 6 = 84

The numbers match up!

Therefore, the original price of p = 72

Answer:

42

Step-by-step explanation:

If 2/7 left that means that 5/7 are still there.

5/7x = 30  Multiple both sides by 7/5

x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]

x = 42

Answer:

final answer would be $6,550

Step-by-step explanation:

To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:

Income Range: $0 - $10,000

Progressive Tax Rate: 3%

Tax Owed: $0 - $10,000 * 3% = $0 - $300

Income Range: $10,001 - $50,000

Progressive Tax Rate: 5%

Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500

Income Range: $50,001 - $100,000

Progressive Tax Rate: 5.5%

Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500

Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.

Yes, the condition that X is normally distributed is satisfied. When a simple random sample is drawn from a population that is normally distributed, the sample will also be normally distributed, as long as the sample size is large enough (generally considered to be at least 30 observations). In this case, the sample size of 36 observations is sufficient to ensure that the sample is normally distributed.

The standard deviation is a useful measure because it allows you to compare the spread of different data sets, even if they have different means. For example, if two data sets have the same mean but one has a larger standard deviation, this suggests that the values in the data set with the larger standard deviation are more spread out or variable.

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The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = [tex]C(n , k) * p^k * (1 - p)^{(n - k)}[/tex]

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = [tex]C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}[/tex]

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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Answer:

4

Step-by-step explanation:

Answer:

The rate of change is 4

Step-by-step explanation:

The rate of change is the slope.

Since the equation is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 4x-3

The slope is 4 and the y intercept is -3

The required values of functions (f₀g)(-3) is 11 and (g₀f)(6) is 23 respectively.

What is a function?

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).

Given, f(x) = 4x - 1

g(x) = |x|

a) (f₀g)(-3) = f(g(-3)) = f(|-3|) = f(3) = 4*3-1 = 11

b) (g₀f)(6) = g(f(6)) = g(4*6-1) = g(23) = 23

Hence, the required values of functions (f₀g)(-3) is 11 and (g₀f)(6) is 23 respectively.

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We get the following answers;

(a) The necessary histogram has been created and is supplied below.

(b) According to the data, it is indeed dangerous to drive close to home. Because 23% and 29% of accidents occur within 1 to 5 miles of home, respectively.

Step 1: in 2001, progressive insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.

Step 2:

Table :

Miles from home          % of accidents      Cumulative

Less than 1                               23                        23

1 to 5                                         29                        52

6 to 10                                       17                         69

11 to 15                                       8                          77

16 to 20                                     6                         83

over 20                                     17                        100

(a) the required histogram is made and attached below.

(b) Yes, the data indicates that driving near home is particularly dangerous. Because, less than , 1 to 5 miles from home 23%, 29% of accidents.

Hence we get the required answers.

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Sales of one store is $274762500 and sales of other store is $275237500.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Given

In a recent year, the total sales at Restaurant A were $475,000 more than at Restaurant B. Total sales at the two stores were $550,000,000.

Let sales of one store be x

Equation,

475000 + x + x = 550,000,000

2x = 550,000,000 - 475000

2x = 549525000

x = 274762500

Sales of one store = $274762500

Sales of other store

= $274762500 + $475000

= $275237500

Sales of one store is $274762500 and Sales of other store is $275237500.

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third side,  AB= 14.318 Units  and  tanB = 0.461

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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Using Pythagoras theorem, Third side,  AB= 14.318 Units  and tanB = 0.461

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius

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

Area of a circle

The formula for the area of a circle is represented as

A = πr²

Express the formula as a product

So, we have the following representation

A = π * r²

In the above formula, we can see that the square of r is multiplied by pi

Hence, the required quantity is the square of the radius of the circle

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The mean time of the entire operation is given by 31 seconds and standard deviation is approximately 4.47 seconds

mean time (μ₁) = 11 seconds

mean chassis time (μ₂) = 20 seconds

a)Total time taken = μ₁ + μ₂ = 11 +20 = 31  seconds

Now we will find the standard deviation:

standard deviation = √ (2²+4²) = √ 20 ≈ 4.47 seconds

b) The probability that the entire process will take less time:

Total time taken = 31 seconds

Less time taken will be 2 seconds for the entire time

P(T<30) = 30 - 31 / 4.47  = - 0.22

Now from the normal distribution table we get the p-value as :

p-value = 0.4129

Hence the required probability is 41.29 % .

The population or sample standard deviation and the standard error of a statistic are not the same thing, but they are related. The standard error of the sample mean is the standard deviation of the set of means computed by drawing an infinite number of repeated samples from the population and computing a mean for each sample.

The mean's standard error is estimated by dividing the sample standard deviation by the square root of the sample size, which matches the population standard deviation divided by the square root of the sample size.

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Answer:

no c is right answer

Step-by-step explanation:

angle b and e should be supplementary

Answer:

A, B and C

Step-by-step explanation:

Statement A

According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.

Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.

Statement B

According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.

Statement C

According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.

Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal [tex]\ell[/tex], then p ║ q.

Statement D

∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary.  However, this does not given enough information to prove p ║ q.

Here, we must use one sample z test for the first question.

Since the population standard deviation is known in this instance. According to the new protein powder firm, it takes an average of 7 days to add 10% more muscle, with a population standard variation of 5.5 days.

Here, keep in mind that the t test should be used if the population standard deviations are unknown and the z test should be used if the population standard deviations are known.

The second question requires that we test the hypothesis to determine whether the MoCA test differs between the days before and after several exposures to a new tool.

Here, a z-test with two samples was utilized. Once the hypothesis has been stated, the z Statistic

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The length of EF in line segment DF is 15.

A line segment's boundaries are two separate places on the same line. Another way to describe a line segment is as a piece of the line that joins two points.

Given that,

Length of line segment DF = 19.

Also, E is any point on line segment,

And DE = 4.

To find the length of EF,

Since, E lies on line segment DF,

Implies that,

DE + EF = DF

4 + EF = 19

EF = 15

The required length of EF is 15.

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The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.

Probability

A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.

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Answer: P/2 - L = W

Step-by-step explanation:

P = 2L + 2W. We are isolating W. Subtract 2L from both sides to isolate the term first
P - 2L = 2W. Divide by 2 on both sides to isolate W.
P/2 - L = W

The number of meals that Boris can feed his dog will be 50 meals.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Boris takes care of his canine with 3/5 pounds of canine nourishment for every dinner. Boris has quite recently purchased 30 pounds of canine food.

The number of meals that Boris can feed his dog will be calculated as,

⇒ 30 ÷ (3/5)

Simplify the expression, then we have

⇒ 30 ÷ (3/5)

⇒ 30 / (3/5)

⇒ 30 x 5 / 3

⇒ 10 x 5

⇒ 50

The number of feasts that Boris can take care of his canine will be 50 dinners.

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Answer:

1) -10x + 5

2) 5p - 26

3) -5y + 6

Answer:

(3,0)

have a nice day.(I needed 20 charecters so yeah i needed to say this)

Answer:

(3,0)

Step-by-step explanation:

The first number in the ordered pair tells us how far we are from the orgina (0,0) (the middle of the graph).  We are 3 units to the right.  The second number in the ordered pair tells us how far up or down from (0,0) we are.  You do not go up for down so that number should be zero.

Answer: B

Step-by-step explanation:

The two equations have the same slope, but different points. This means that the lines are parallel to one another and will not intersect.

The answer is B: No solution

Answer: No solution.

Step-by-step explanation: I graphed the two given functions below.  It looks like there is no solution to the given functions.

Hope this helps! :)

Based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem and t=2

The given parameters are

t: 2≤t≤4

t is a continuous function between 2≤t≤4

We should equally know that the amount of coffee at the cup at a time y=C

Using the formula  for t

t=C(4) -C(2)/4-2

Inputting the values of t at the extremes values

t=C(4) -C(2)/4-2  = (12.8-8.8)/4-2

Simplifying this to get

4/2

=2

⇒ C(2) is continuous on the coordinates (2,4) and this can be differentiated in the coordinates (2,4)

If we apply the intermediate value theorem, the is t in (2,4)

Therefore, C(t) = [C(4)- C(2)]/ 4-2

This implies that C(t) = 2

In conclusion, based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem. and t=2

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Answer:

first option

Step-by-step explanation:

using the property of logarithms

ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )

given

[tex]17^{(0.3x+5)}[/tex] = 12

take the ln of both sides

ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then

(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )

0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )

0.3x ≈ - 4.12293 ( divide both sides by 0.3 )

x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )

Answer:

the circumference of the circle is 6.28metres

Step-by-step explanation:

diameter=2m

circumference=2πr or πd

it is a diameter so use the formula πd

take π=22/7 or 3.14

c=22/7×2m=44/7=6.28m