Sara is considering charging her electric car. If she goes to the charging station on the following map, she will have to drive farther than if she drove straight to her destination. How much shorter is the path straight to the destination than past the charging station?​

Answer:

A. The triangles are congruent by SAS.

Step-by-step explanation:

Two sides of one triangle are congruent to two sides of the other triangle. The included angles of the two triangles are congruent.

The triangles are congruent by SAS.

Therefore, based on their z-scores, Ryan is more likely to be accepted at his university of choice than Kyle, assuming that the admissions decision is based solely on their exam scores.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. The closer the probability is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely it is to occur.

Here,

To determine which of the two students is more likely to be accepted at their university of choice, we need to compare their exam scores relative to the other students who took the same exam. We can use the concept of standard scores, also known as z-scores, to make this comparison.

The z-score of an observation x is the number of standard deviations that x is away from the mean of the population. It is calculated as:

z = (x - μ) / σ

where x is the observation, μ is the mean of the population, and σ is the standard deviation of the population.

For Kyle's exam, his z-score is:

z = (403 - 355) / 59 = 0.814

For Ryan's exam, his z-score is:

z = (45 - 27) / 4 = 4.5

A z-score of 0 means the observation is at the mean of the population, while a positive z-score means the observation is above the mean, and a negative z-score means the observation is below the mean.

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

Answer:

it would be 144

Answer:

9

Step-by-step explanation:

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

To know more about depreciation, refer here:

https://brainly.com/question/30531944

#SPJ11

The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

learn more about gain here:

https://brainly.com/question/31218742

#SPJ11

But the diamerter equals d, so 6.

Answer:

its 6

Step-by-step explanation:

because your finding the diameter.

Concept and uses of image translation are explain below.

In math, a change is an activity that moves, flips, or changes a shape (called the preimage) to make another shape (called the picture). An interpretation is a sort of change that moves each point in a figure a similar distance in a similar course.

An interpretation is a kind of change that takes each point in a figure and slides it a similar distance in a similar course. This interpretation maps △ X Y Z \triangle{XYZ} △XYZtriangle, X, Y, Z onto the blue triangle. The outcome is another figure, called the picture. The picture is consistent to the first figure.

To know more about image translation visit:

brainly.com/question/17826211

#SPJ4

The value of x, y and z in the rhombus are 9, 2 and -4.

A rhombus is a quadrilateral that has 4 sides congruent to each other. The sum of angles in a rhombus is 360 degrees.

Therefore, let's find the value of x, y and z in the rhombus as follows:

Hence,

10y + 3 = 23

10y = 23 - 3

10y = 20

y = 20 / 10

y = 2

Therefore,

3x - 4 = 23

3x = 23 + 4

3x = 27

x = 27 / 3

x = 9

-6z - 1 = 23

-6z = 23 + 1

-6z = 24

divide both sides by -6

z = 24 / -6

z = -4

learn more on rhombus here: brainly.com/question/28709089

#SPJ1

Answer: 0.01 = 10-2 .

Step-by-step explanation: have a good day!

The pH of a 0.10M Tris-acid solution is 4.65.

pH: The pH of a solution is the negative logarithm (base 10) of the hydrogen ion concentration in moles per liter. In other words, it is a measure of the acidity or basicity of a solution. The pH scale ranges from 0 to 14, where 7 is neutral, less than 7 is acidic, and greater than 7 is basic or alkaline.What is the pH of a 0.10 M Tris-base solution? (pH 10.65)For the reaction, Tris-base + H₂O ↔ Tris-acid + OH⁻, the pKb of Tris-base can be computed as: pKb + pKa = 14pKb = 14 - pKa = 14 - 8.30 = 5.7Thus, Kb = antilog (-5.7) = 1.995 x 10⁻⁶, which is the equilibrium constant for the reaction Tris-base + H₂O ↔ Tris-acid + OH⁻[OH⁻] = Kb x [Tris-base] / [H₂O] = 1.995 x 10⁻⁶ x 0.10 / 1000 = 1.995 x 10⁻⁷pH = 14 - pOH = 14 - (-log[OH⁻]) = 14 - (-log(1.995 x 10⁻⁷)) = 10.65Therefore, the pH of a 0.10M Tris-base solution is 10.65.What is the pH of the solution after mixing 35.0 mL0.10M Tris-base with 2.50 mL of 1.00 M HCl. The pKa of Tris-acid is 8.30 at 25°C. (pH7.90)The balanced chemical equation is Tris-base + HCl ↔ Tris-acid + Cl⁻Initial concentration of Tris-base = (35.0 / 37.50) x 0.10 = 0.0933 MInitial concentration of HCl = (2.50 / 37.50) x 1.00 = 0.0667 MInitially, the mixture was a buffer solution with a pH of:pH = pKa + log([A⁻] / [HA])pH = 8.30 + log(0.0933 / 0.00667) = 9.35The number of moles of Tris-base and HCl can be calculated as follows:Number of moles of Tris-base = 35.0 / 1000 L x 0.10 mol / L = 0.0035 molNumber of moles of HCl = 2.50 / 1000 L x 1.00 mol / L = 0.0025 mol

The limiting reagent in the reaction is HCl, and all of it will be used up. Tris-base will be converted to Tris-acid. Therefore, the number of moles of Tris-base remaining will be:Number of moles of Tris-base remaining = 0.0035 mol - 0.0025 mol = 0.0010 molSince the volume of the mixture is 37.5 mL, the concentration of Tris-acid is 0.0010 mol / 0.0375 L = 0.0267 M.The concentration of Cl⁻ in the mixture is 0.0667 M, and the concentration of Tris-base remaining is 0.0010 M. Therefore, the concentration of OH⁻ can be calculated as follows:[OH⁻] = Kw / [H⁺] = 1.0 x 10⁻¹⁴ / 0.0667 = 1.50 x 10⁻¹³The pH of the mixture is:pH = pKa + log([A⁻] / [HA])pH = 8.30 + log(0.0010 / 0.0267) = 7.90Therefore, the pH of the solution after mixing 35.0 mL0.10M Tris-base with 2.50 mL of 1.00 M HCl is 7.90.What is the pH of a 0.10M Tris-acid solution? (pH 4.65)The pKb of Tris-acid can be calculated as:pKb + pKa = 14pKb = 14 - pKa = 14 - 8.30 = 5.7Kb = antilog (-5.7) = 1.995 x 10⁻⁶The Kb for Tris-acid can be used to calculate the concentration of OH⁻:[OH⁻] = Kb x [HA] / [H₂O] = 1.995 x 10⁻⁶ x 0.10 / 1000 = 1.995 x 10⁻⁷The pH of the solution can be calculated as:pH = 14 - pOH = 14 - (-log[OH⁻]) = 14 - (-log(1.995 x 10⁻⁷)) = 4.65Therefore, the pH of a 0.10M Tris-acid solution is 4.65.

Learn more about pH :

https://brainly.com/question/2288405

#SPJ11

Step-by-step explanation:

..............

=> 3x + 4y = 12

Answer:

-3t+30

Step-by-step explanation:

The equation of remaining chocolate C  in terms of t is C =30 - 3t.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C =30 - 3t.

To know more about Equation on:

https://brainly.com/question/187506

#SPJ2

Answer:

4

Step-by-step explanation:

1 5

2 10

3 15

4 20

i wrote it out

x+16=5x

16=4x

4=x

Marissa is currently four years old.

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use.

Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.

Let's represent Marissa's current age "x".

According to the given question, in 16 years she will be five times older than she is today, which we can express as:

x + 16 = 5x

Solving for x, we can subtract x from both sides:

16 = 4x

Dividing both sides by 4, we get:

x = 4

Therefore, Marissa is currently 4 years old.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ6

Answer:

697.45

Step-by-step explanation:

interest for the first year = 13.5 % of 580 = 78.3

for 0.5 year, it will be 78.3 /2 =39.15

1year + 0.5 year = 78.3 + 39.15= 117.45

add that to borrowed amount to get total amount paid

117.45+ 580= 697.45

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

- The distributive property is a basic algebraic property that allows us to distribute a factor to each term inside a set of parentheses. It states that for any real numbers a, b, and c:

- This means that you can multiply a number or variable by a sum or difference by multiplying each term inside the parentheses separately, and then adding or subtracting the resulting products. For example:

\(\qquad\begin{aligned}\sf 3(2 + 5)& =\sf 3(2) + 3(5)\\& =\sf 6 + 15\\&=\sf 21\end{aligned}\)

- This property is useful in simplifying algebraic expressions and solving equations.

To simplify \(\sf y = (x+1)(x+2)\), we use the distributive property of multiplication:

\(\qquad\begin{aligned}\sf y& =\sf x(x+2) + 1(x+2)\\& =\sf x^2 + 2x + x + 2\end{aligned}\)

Now we combine like terms:

Therefore, the simplified form of \(\sf y = (x+1)(x+2)\) is \(\bold{y = x^2 + 3x + 2}\).

To learn more about the distributive property, visit this link below:

Answer:

256/5=51.2

Step-by-step explanation:

Answer:

51 with a remainder of one, or 51.2

Step-by-step explanation:

She has 256 donuts and 5 friends. I assume this is for long division practice, so I will do long division.

5 | 256

Look at the first term. Does 5 go into 2? No. Bring down the next term.

5|256

  25

Does 5 go into 25? Yes! How many times? 5. The first digit of our answer will be 5.

5|256 = 5

  25

Now to get rid of the 25, we multiply the number we took for our answer by the divisor. 5x5 = 25. Subtract this from 25 and bring down the next (and last term).

5|256 = 5

  25

 -25

     06

Does 5 go into 6? Yes. One time. Repeat what we did just now with this term now.

5|256 = 51

  06

   -5

     1

Does 5 go into 1? No, it is smaller. Therefore we have a remainder of one donut.

If we are trying to divide ALL of the donuts equally, we will have to cut up the donut into 5 equal pieces. They would each be 1/5 of the donut, or 0.2.

So adding this, each friend would get 51 donuts, with an extra donut for Mrs Rivas, or each friend would get 51.2/51 and 1/5 donuts.

Answer:

     [-9,0]

Step-by-step explanation:

Look along the y inercept and find where the lines end

plus they are solid circles so it'd be closed

Answer: see below

Step-by-step explanation:

The range is the set of possible output values shown on the y-axis.

This graph's maximum y value, or the highest y value, is 0. The lowest y value is -9

R:yE[-9,0]

Answer:

Jacob got 18 votes.

Hope this helps :)

The correct answer is 113. To forecast the sales of the ice rink on day 4 using the trend method, we need to determine the trend equation based on the given data points.

The trend equation represents the overall pattern or trend in the sales data and allows us to make predictions for future values.

First, we need to calculate the average increase in sales per day. The average increase is obtained by dividing the total increase in sales over the three days (102 - 80 = 22) by the number of days (3 - 1 = 2). Therefore, the average increase in sales per day is 22 / 2 = 11.

Next, we can use the average increase to forecast the sales for day 4. Starting from the last known sales value (102), we add the average increase to project the sales for the next day. Thus, the forecasted sales for day 4 would be 102 + 11 = 113.

Therefore, the correct answer is 113.

Learn more about average here:
brainly.com/question/27646993

#SPJ11

The vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.

A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function. The equation of a parabola in standard form is y = ax² + bx + c, where "a", "b", and "c" are constants, and "x" and "y" are variables.

a. To evaluate h(0), we substitute t=0 in the equation:

h(0) = 15 + 7(0) - 16(0)² = 15

This means that at the instant the boy throws the rock (t=0), the height of the rock is 15 feet above the ground.

b. To estimate the time when the rock hits the ground, we need to find the value of t when h(t) = 0. We can solve the equation 15 + 7t - 16t² = 0 for t, using the quadratic formula:

t = (-7 ± √(7² - 4(-16)(15))) / (2(-16))

t ≈ 1.28 s or t ≈ 1.97 s

This means that the rock will hit the ground approximately 1.28 seconds or 1.97 seconds after it is thrown.

c. The equation h(1) = 6 means that one second after the rock is thrown, its height above the ground is 6 feet.

d. The vertex of the parabola h(t) = 15 + 7t - 16t² can be found by using the formula t = -b/2a, where a=-16 and b=7.

t = -7 / (2(-16)) = 7/32

Substituting t=7/32 into the equation, we get:

h(7/32) = 15 + 7(7/32) - 16(7/32)² ≈ 17.2

Therefore, the vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.

To know more about parabola visit:

https://brainly.com/question/10572747

#SPJ1

Answer:

m2+2m-8=0 Two solutions were found : m = 2 m = -4 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1.1 Factoring m2+2m-8 The first term is, m2 its ...

Step-by-step explanation:

The equation \(x^2 + y^2 + 10y + 20 = 0\) represents a circle with center (0, -5) and radius 5.

To determine if the equation represents a circle, we need to rewrite it in standard form. The standard form of a circle equation is \((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center of the circle and r represents the radius.

Completing the square for the y terms:

\(x^2 + y^2 + 10y + 20 = 0\\ x^2 + y^2 + 10y = -20\\ x^2 + y^2 + 10y + 25 = -20 + 25\\ x^2 + (y + 5)^2 = 5\)

Now the equation is in standard form, \((x - 0)^2 + (y + 5)^2 = 5^2\), which represents a circle.

By comparing the equation to the standard form, we can determine the center and radius of the circle. The center is given by the values (h, k), which in this case is (0, -5). Therefore, the center of the circle is (0, -5).

The radius is determined by the term \(r^2\), which in this case is \(5^2 = 25\). Therefore, the radius of the circle is 5.

In summary, the equation x^2 + y^2 + 10y + 20 = 0 represents a circle with center (0, -5) and radius 5. The completion of the square allowed us to rewrite the equation in standard form, making it evident that it represents a circle. The center of the circle is determined by the values of x and y, and the radius is determined by the value of r.

Learn more about circle equation here:

https://brainly.com/question/29104982

#SPJ11

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer: C: y=1.15x + 10.95

Step-by-step explanation:

look it up

The graph of the sequence may pass toward the vertical line test.

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

Given the information that, he gives two away on day 1, four away on day 2, and eight away on day 3. He continues this pattern for 10 days.

Let x be the number of days and f(x) be the number of cards.

So, the pattern is

f(x)=2, when x=1

f(x)=4, when x=2

f(x)=8, when x=3

Then, the function will be f(x)=2ˣ

The equation of the graph is passing through a vertical line.

The vertical line test is a graphical method that determines whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

To learn more about the function:

https://brainly.com/question/8366971

#SPJ4

Using tautology, we can conclude that the argument here is invalid.

A compound statement known as a tautology is one that is true regardless of whether the individual statements inside it are true or false.

The Greek term "tautology," which means "same" and "logy," is where the word "tautology" comes from.

We need to build a truth-table and examine the truth value in the last column in order to determine whether a particular statement is a tautology.

It is a tautology if all of the values are true.

In the given case:

p is TRUE

and

q is FALSE

In this case:

p→q : is FALSE (the assumption “TRUE implies FALSE” is FALSE)

So, here:

p → (p→q) is equal to as p → FALSE

But p is TRUE so in that case it’s TRUE→ FALSE, which is in fact FALSE.

Since there a case where the expression is not true, then it’s not valid.

It’s invalid.

Learn more about tautology here

brainly.com/question/30195011

#SPJ4

Given question is incomplete, the complete question is below

Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.

the height of the tower gives a ratio of 159/155. Taking the inverse tangent of this ratio gives the angle of elevation of the sun, 56.7°.

Let x represent the sun's elevation angle.Then, tan(x) = 159/155.

x = tan-1(159/155) = 56.7°

The angle of elevation of the sun can be calculated using the tangent ratio. The tangent ratio states that the opposite side divided by the adjacent side of a triangle is equal to the tangent of the angle. In this case, the opposite side of the triangle is the length of the shadow, 159 feet, and the adjacent side is the height of the tower, 155 feet. Dividing the length of the shadow by the height of the tower gives a ratio of 159/155. Taking the inverse tangent of this ratio gives the angle of elevation of the sun, 56.7°.

Learn more about angle here

https://brainly.com/question/28451077

#SPJ4

Answer:

ii guess 18

Step-by-step explanation:

One book costs $18.

        \(7x + 17 = 143\)

        \(7x + 17 = 143\)

        (minus 17 on both sides)

        \(7x = 126\)

        (divide both sides by 7)

        \(x = 18\)