Lo is leaving from work today at 6:15 p.m. She has errands to run before she meets her friends for dinner at 8 p.m. If it takes Lo of an hour to run each errand, how many errands does she have time to run between work and dinner?

Answer: [tex]57\°[/tex]

Step-by-step explanation:

For this exercise it is important to remember that:

1. The word "difference" indicates subtraction (The result of a subtraction is called "difference").

2. The multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

For this case, according to the data given in the exercise, the records high temperature and the record low temperature are:

[tex]High\ temperature=41\°\\\\Low\ temperature=-16\°[/tex]

Therefore, if you want to find the difference in the record temperatures, you need to sutract them.

Then you get the following result:

[tex]High\ temperature-Low\ temperature=41\°-(-16\°)=41\°+16\°=57\°[/tex]

Answer:

Speed of car A = 40 mph

Speed of car B =  50 mph

Step-by-step explanation:

Given:

Distance travelled by car A  = 120 miles

Distance travelled by car B  =  120 miles

To Find:

speed of each car = ?

Solution:

Let the speed of car A be x

then  speed of car B is (x +10)

The Time taken for each car is same

Time taken for car A =  Time taken for car B

We know that time  = [tex]\frac{distance}{speed}[/tex]

Time taken for car A

=> [tex]\frac{120}{x}[/tex]---------------------------(1)

Similarly

Time taken for car B

=> [tex]\frac{150}{x+10}[/tex]-----------------------(2)

Equating (1) and (2), we get

[tex]\frac{120}{x}[/tex] =  [tex]\frac{150}{x+10}[/tex]

[tex]120 \times (x+10) = 150 \times x[/tex]

120x + 1200 = 150x

1200 = 150x-120 x

1200 = 30x

[tex]x= \frac{1200}{30}[/tex]

x= 40

Speed of car A = 40mph

Speed of car B = (x+10) = (x+40) = 50mph

The answer is 63.because it can be divided by other many numbers like 3,7,9 ......

I am 100% sure about the answer..

Answer:

B. 63.

Step-by-step explanation:

Because 63 can be written as a multiple of smaller numbers .

For example 7 * 9 = 63.

Answer:

[tex]\displaystyle x=-15[/tex]

Step-by-step explanation:

Solution Of A System Of Equations

A system of linear equations is given as

[tex]\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]

There are many methods to solve them. We will use the method of reduction

The given system is

[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.[/tex]

Multiplying the second equation by -3

[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.[/tex]

Adding the resulting equations

[tex]\displaystyle -x=15[/tex]

[tex]\displaystyle x=-15[/tex]

Answer:

5/2=2.5, while 1/3= aprox 0.333, therefore 5/2 is not equal to 1/3.

Step-by-step explanation:

Here is the long division table for 5/2

 2. 5 0 0

2 5. 0 0 0

− 4      

 1 0    

− 1 0    

   0 0  

 −   0  

     0 0

   −   0

       0

Here is the long division table 1/3 ( to three decimal places)

0. 3 3 3

3 1. 0 0 0

− 0      

 1 0    

−   9    

   1 0  

 −   9  

     1 0

   −   9

       1

An easier way to do 5/2 is to think of 50/2, which is 25, and then add a decimal point, making it 2.5.

An easier way to do 1/3 is to think of it as one third (of one), or 0.333 repeating.

Answer: options C and D

Step-by-step explanation:

An Irrational Number is a real number that cannot be written as a simple fraction.

A . 2/3 is a rational number because it is a fraction

B . -[tex]\sqrt{81}[/tex] = -9 which could be written as -9/1 , so it is a rational number

C. 5.76262... is irrational because the decimal has no end point

D. [tex]\sqrt{2}[/tex] is a common example of irrational number , because finding the square root of 2 is also continuous .

Therefore , options C and D are irrational

Investing $2500 annually for 10 years into an annuity with a 3.4% APR yields approximately $31,790.56, making option B the correct choice.

A recurring-payment variable annuity typically involves regular contributions over time, often with variable returns based on market performance. Option B seems to fit this description best: "An annuity with an APR of 3.4% into which you invest $2500 each year."

To calculate the future value of this annuity, we can use the formula for the future value of an annuity:

FV = Pmt × [(1 + r)^n - 1] / r

Where:

FV = Future value

Pmt = Payment per period ($2500)

r = Interest rate per period (3.4% or 0.034)

n = Number of periods (number of years)

Let's assume we invest for 10 years:

[tex]FV = 2500 * [(1 + 0.034)^10 - 1] / 0.034[/tex]

Calculating this gives us approximately $31,790.56.

Therefore, investing $2500 each year for 10 years into an annuity with an APR of 3.4% would result in a future value of approximately $31,790.56.

Final answer: B. An annuity with an APR of 3.4% into which you invest $2500 each year.

The Correct question is:

Which of these is an example of a recurring-payment variable annuity?

A. An annuity with a minimum APR of 3.4% into which you invest a lump sum of $12,500

B. An annuity with an APR of 3.4% into which you invest $2500 each year C. An annuity with a minimum APR of 3.4% into which you invest $2500 each year

D. An annuity with an APR of 3.4% into which you invest a lump sum of $12,500

2*k + 3 = 13

2*k = 13 - 3

2*k = 10

k = 10/2

k = 5

The verbal statement 'Three more than twice k is thirteen' translates into the mathematical equation 2k + 3 = 13. Solving this equation, we find that k equals 5. This is an example of forming and solving an algebraic equation from a word problem.

The question asks to translate a verbal statement involving a variable into a mathematical equation. The statement is 'Three more than twice k is thirteen.' To form an equation, we first identify the mathematical operations described in the statement. 'Twice k' means we need to multiply k by 2, so we have 2k. 'Three more than' suggests an addition of 3 to the previous result, so we add 3 to 2k to get 2k + 3. Finally, 'is thirteen' tells us that this expression is equal to 13. The equation becomes 2k + 3 = 13.

To solve for k, we subtract 3 from both sides to obtain 2k = 10, and then divide by 2, resulting in k = 5. This completes the exercise of writing and solving the equation.

Example of a similar equation:

Let's say we have 'Four less than half of x is twenty.' The equation would be (1/2)x - 4 = 20. We would solve by adding 4 to get (1/2)x = 24, and then multiply by 2 to find x = 48.

Answer:

[tex]y=-\frac{5}{3}x+1[/tex]

Step-by-step explanation:

Given:

Equation of the line.

[tex]3x-5y=5[/tex]

And passes through the point (9, -14)

Solution:

Now, we have to write an equation that is perpendicular to 3x -5y = 5 and passes through the point (9, -14).

Now, we write the given equation in [tex]y=mx+b[/tex] form.

[tex]3x-5y=5[/tex]

[tex]5y=3x-5[/tex]

[tex]y=\frac{3}{5}x-\frac{5}{5}[/tex]

[tex]y=\frac{3}{5}x-1[/tex]

So, the slope of the line is [tex]m=\frac{3}{5}[/tex].

The slope of the perpendicular line is [tex]-\frac{1}{m}[/tex]

now, we substitute m value in above relation.

[tex]=-\frac{1}{\frac{3}{5}}[/tex]

[tex]=-\frac{5}{3}[/tex]

So the equation of the perpendicular line is:

[tex]y=-\frac{5}{3}x+b[/tex]--------(1)

Lets us find  b from the given points (9, -14).

[tex]-14=-\frac{5}{3}\times 9+b[/tex]

[tex]-14=-5\times 3+b[/tex]

[tex]-14=-15+b[/tex]

[tex]b=15-14[/tex]

[tex]b=1[/tex]

Now, we substitute b value in equation 1.

[tex]y=-\frac{5}{3}x+1[/tex]

Therefore, the equation of the perpendicular line is

[tex]y=-\frac{5}{3}x+1[/tex]

The equation of the line that is perpendicular to 3x - 5y = 5 passing through the point (9, -14) is y = -5x/3 + 1.

To find the equation of a line that is perpendicular to a given line, we first need to find the slope of the given line. The equation in the question is given in standard form (Ax + By = C), so we need to convert it into slope-intercept form (y = mx + b), where m is the slope. In slope-intercept form, the given equation becomes y = 3x/5 + 1.

The slope of this line is 3/5. The slope of a line perpendicular to this one is the negative reciprocal, or -5/3. This is because the product of the slopes of two perpendicular lines is -1.

We now know that the equation of the line perpendicular to the given one has the form y = -5x/3 + b. To find b (the y-intercept), we can use the point that the line has to pass through (9, -14). We substitute these values into the equation, and solve for b. This gives: -14 = -5(9)/3 + b. Solving for b gives, b = -14 + 15 = 1.

Therefore, the equation of the line perpendicular to 3x - 5y = 5 passing through the point (9, -14) is y = -5x/3 + 1.

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Answer:

wouldn't it just be [tex]\frac{10}{11} x[/tex]

Step-by-step explanation:

this is also: [tex]\frac{-10*x}{-11}[/tex]

which is why it simplifies to the answer

Answer:

(1). 110 followers

(2). 463 days

(3). Days since upload                0 10 20 50 100 300 500

Number of Instagram followers 100 122 149 270 732 39158 2,000,000

(5) [tex]f(x)=100(1.03)^d[/tex]

Step-by-step explanation:

Part 1:

The function that represents the situation is:

[tex]f(x) = 100(1 .01)^{2d}[/tex]

Where [tex]d[/tex] is number of days.

Using this equation we find the number of followers after 5 days:

[tex]f(d) = 100(1 .01)^{2*5}=110[/tex] followers.

Part 2:

We solve the equation

[tex]1,000,000 = 100(1 .01)^{2d}[/tex]

for [tex]d[/tex] and get:

[tex]d=463\: days.[/tex]

It takes Alexis 463 days to reach 1,000,000 followers.

Part 3:

Days since upload                0 10 20 50 100 300 500

Number of Instagram followers 100 122 149 270 732 39158 2,000,000

This is obtained from the graph of the function f(x).

Part 4:

The number of Instagram followers increases fast because the rate of increase is 1% of the previous number of followers, and as the followers increase, this 1% takes increasingly big values, leading to increasingly fast growth rate of followers. Put simply, we would say that f(x) is an exponential function.

Par 5:

If the rate is increased to 3% every 24 hours, then the function f(x) becomes:

[tex]f(x)=100(1.03)^d[/tex]

where [tex]d[/tex] is days. and if we represent this in terms of every 12 hours then

[tex]f(x)=100(1.03)^{t/2}[/tex]

where [tex]t[/tex] is every 12 hours.

it is very easy.I will explain u...

between 1 and 3 3 is greater..so we have put the plus sign and multiply + and - it wil ne - so that we have subtracted it...Hope it helps u...

Answer:

[tex]\displaystyle x = 8[/tex]

Step-by-step explanation:

Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.

I am joyous to assist you anytime.

Answer:

Easiest—divide by 100: The simplest way to convert a percentage to a decimal is to divide the number (in percentage format) by 100

Move the decimal: Another way to convert a quoted percentage to decimal format is to move the decimal two places to the left. Remember, if you don’t see a decimal, just imagine that it’s at the end, or far right side, of the number. Imagine that the decimal is followed by two zeroes if that helps.

Step-by-step explanation:

Answer:

Converting Percentages to Decimals

Easiest—divide by 100: The simplest way to convert a percentage to a decimal is to divide the number (in percentage format) by 100.

Move the decimal: Another way to convert a quoted percentage to decimal format is to move the decimal two places to the left.

hope this helps

can you help me with this

The war of wall | Why is the wall special to the narrator and Lou?

The relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.

In a dilation, lines that pass through the center of dilation (the point about which the dilation occurs) remain unchanged.

This means that the line WX and its corresponding line W'X' would be collinear and have the same length if they pass through the center of dilation.

If the larger figure was dilated using a scale factor of 4, it means that every point in the larger figure is four times farther from the center of dilation than its corresponding point in the smaller figure. In this case, line WX would be four times longer than line W'X', and they would be parallel since they maintain the same direction.

So, the relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.

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Answer:

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

From the picture we have

[tex]b_1=19yd,\ b_2=5yd,\ h=9yd[/tex]

Substitute:

[tex]A=\dfrac{19+5}{2}\cdot9=\dfrac{24}{2}\cdot9=12\cdot9=108\ yd^2[/tex]

Answer:

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) [tex]\$68.76[/tex]

Part 4) [tex]\$12\ per\ hour[/tex]

Part 5) The equation that can be used is [tex]27x=242.73[/tex]  and the cost of one print is [tex]\$8.99[/tex]

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$10\ per\ class[/tex]

The y-intercept is [tex]b=\$100[/tex]

so

[tex]y=10x+100[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$15\ per\ class[/tex]

so

[tex]y=15x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]10x+100 < 15x[/tex]

Solve for x

subtract 10 x both sides

[tex]100 < 15x-10x[/tex]

[tex]100 < 5x[/tex]

Divide by 5 both sides

[tex]20 < x[/tex]

Rewrite

[tex]x > 20[/tex]

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

[tex]8+3x=23[/tex]

solve for x

subtract 8 both sides

[tex]3x=23-8[/tex]

[tex]3x=15[/tex]

Divide by 3 both sides

[tex]x=5[/tex]

Part 3) we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is [tex]m=\$0.42\ per\ mile[/tex]

The y-intercept is [tex]b=\$36[/tex]

so

[tex]y=0.42x+36[/tex]

For x=78 miles

substitute in the linear equation and solve for y

[tex]y=0.42(78)+36[/tex]

[tex]y=\$68.76[/tex]

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

[tex]40x+10(1.5x)=660[/tex]

solve for x

[tex]40x+15x=660[/tex]

[tex]55x=660[/tex]

Divide by 55 both sides

[tex]x=\$12\ per\ hour[/tex]

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

[tex]27x=242.73[/tex]

solve for x

Divide by 27 both sides

[tex]x=\$8.99[/tex]

Part 6) we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$7\ per\ class[/tex]

The y-intercept is [tex]b=\$120[/tex]

so

[tex]y=7x+120[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$11\ per\ class[/tex]

so

[tex]y=11x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]7x+120 < 11x[/tex]

Solve for x

subtract 7x both sides

[tex]120 < 11x-7x[/tex]

[tex]120 < 4x[/tex]

Divide by 4 both sides

[tex]30 < x[/tex]

Rewrite

[tex]x > 30[/tex]

therefore

The number of classes must be greater than 30

Answer:

The students who have a cell phone and can use social media are 3.

Step-by-step explanation:

The question is incomplete so the complete question is:

There are 30 students in Mrs. Bailey’s class, and 1/5 of the class has their own cell phone. Of this group of students, 1/2 of them are allowed to use social media. How many of the students have a cell phone and can use social media?

Now, as given in question we need to find the number of students have a cell phone and can use social media.

Now, to get the number of students of the class who has their own cell phone:

[tex]\frac{1}{5}\ of\ 30.[/tex]

[tex]=\frac{1}{5} \times 30.[/tex]

[tex]=\frac{30}{5}[/tex]

[tex]=6.[/tex]

Of this group of 6 students, 1/2 of them are  allowed to use social media.

So, to get the number of students who use social media:

[tex]\frac{1}{2}\ of\ 6.[/tex]

[tex]=\frac{1}{2} \times 6[/tex]

[tex]=\frac{6}{2}[/tex]

[tex]=3.[/tex]

Therefore, the students who have a cell phone and can use social media are 3.

The required criteria for congruence is SSS criteria.

Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.

From the given figure for the two triangles,

It is clear that the corresponding sides for both the triangles are equal.

Thus, both the triangles satisfy the congruence criteria os SSS.

Hence, the given two triangles are congruent by the SSS criteria.

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Answer:

Step-by-step explanation:

Givens

Area = L * w

w = x

l = x  + 4

Area = 32

Solution

32 = x(x + 4)

32 = x^2 + 4x

x^2 + 4x - 32

(x + 8)(x - 4)

Only x - 4 is going to make any sense

x - 4 = 0

x = 4

The width is 4

The length is 4 + 4 = 8

4*8 = 32 which is the area.

Final answer:

To find the length and width of the barn wall, set the width as w and form a quadratic equation w(w + 4) = 32. Solve the equation to find that the width is 4 feet and the length is 8 feet.

Explanation:

The student is asking how to find the length and width of a rectangular barn wall when the area is given (32 square feet) and the length is 4 feet longer than the width. To solve this, let's represent the width of the wall as w feet. Thus, the length will be w + 4 feet. The area of a rectangle is found by multiplying the length by the width, which gives us the equation w(w + 4) = 32.

Let's solve this quadratic equation:

Rewrite the equation: w² + 4w = 32.

Subtract 32 from both sides to set the equation to zero: w² + 4w - 32 = 0.

Factor the quadratic equation: (w + 8)(w - 4) = 0.

Solve for w: w = -8 (reject because width can't be negative) or w = 4 (accept).

Thus, the width of the wall is 4 feet and the length is 4 + 4 = 8 feet.

Answer:

[tex]\$36.25+\$3.89x\le \$58.50[/tex]

Step-by-step explanation:

Let x be the number of folders with paper Jessica buys. If Jessica buys x folders for $3.89 each, then she pays $3.89x for all x folders.

She wants to buy one backpack for $36.25, so her total buying costs

$36.25 + $3.89x

Jessica saved a total of $58.50 to spend on school supplies, then her total buying cannot exceed this sum, so

[tex]\$36.25+\$3.89x\le \$58.50[/tex]

Answer:

y=-1/5x+1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-2)/(10-(-5))

m=-3/(10+5)

m=-3/15

m=-1/5

y-y1=m(x-x1)

y-2=-1/5(x-(-5))

y-2=-1/5(x+5)

y=-1/5x-5/5+2

y=-1/5x-1+2

y=-1/5x+1

Answer:

The correct answer is C. 20.33%

Step-by-step explanation:

1. Let's review all the information given to us to answer the question correctly.

Mean of time of adults walking a mile = 22 minutes

Standard deviation = 6 minutes

Normal distribution for the walking times

2. What percentage of adults take longer than 27 minutes to walk a mile?

27 minutes = Mean + 5 minutes

27 minutes = Mean + 0.83 * Standard deviation

Using the z table for z = 0.83, we have that:

P (z) = 0.7967

Therefore the probability of adults that take longer than 27 minutes walking a mile is:

1 - 0.7967 = 0.2033

The correct answer is C. 20.33%

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis.

According to the statement data we have:

[tex]m = \frac {7} {3}[/tex]

Thus, the equation is of the form:

[tex]y = \frac {7} {3} x + b[/tex]

We substitute the given point and find the cut-off point:

[tex]- \frac {35} {3} = \frac {7} {3} (0) + b\\- \frac {35} {3} = b[/tex]

Finally, the equation is:

[tex]y = \frac {7} {3} x- \frac {35} {3}[/tex]

We manipulate algebraically to obtain the standard form:

We multiply by 3 on both sides of the equation:

[tex]3y = 7x-35\\3y-7x = -35[/tex]

We multiply by -1 on both sides:

[tex]7x-3y = 35[/tex]

Answer:

[tex]7x-3y = 35[/tex]

The cost of one candy is 66 cents.

Step-by-step explanation:

Given,

Purchase price of box of candies = $10.54

Number of candies in the box = 16

To find the cost of each candy, we will divide the purchase price of candies with total number of candies.

Cost of each candy = [tex]\frac{10.54}{16}[/tex]

Cost of each candy = $0.658

Rounding off to nearest hundredth;

Cost of each candy = $0.66 = 0.66 * 100 = 66 cents

The cost of one candy is 66 cents.

Keywords: division, multiplication

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Answer:

let the scone be x and the large coffees be y.

7x+4y=$25.76-----equ(I)

2x+5y=$14.92-----equ(2)

make x the subject of the formulae in equation(ii).

x=$14.92/2-5y

x=7.46-5y

Answer:

Step-by-step explanation:

Answer:

8/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-1)/(2-5)

m=-8/-3

m=8/3

Answer:

∠ABC = 110°

Step-by-step explanation:

Since Δ BCD is equilateral then the 3 angles are congruent with measure 60°

Thus ∠ DBC = 60°

Δ ABD is isosceles with AB = BC

Thus the base angles are congruent, that is

∠ BAD = ∠ ADB = 65°

Calculate ∠ ABD by subtracting the sum of the base angles from 180°

∠ ABD = 180° - (65 + 65)° = 180° - 130° = 50°

Hence

∠ ABC = ∠ ABD + ∠ DBC = 50° + 60° = 110°

Answer:

110°

Step-by-step explanation:

Triangle ABD is an isosceles triangle.

This means that ∠ ADB is also 65°

Use the Triangle Sum Theorem (All angles of a triangle sum up to 180°)

65 + 65 = 130

180 - 130 = 50

∠ ABD is 50°

For Triangle BCD, all of the sides are the same.

This means all of the angles will be 60° (60° * 3 = 180°)

To find ∠ ABC, you add the two angles

60° + 50° = 110°

Answer:

y = 3x + 22

Step-by-step explanation:

y - 7 = 3(x+5)

Distribute,

y - 7 = 3x + 15.

Add 7 to both sides.

Final answer, y = 3x + 22.

Hope this helps!

Answer:

22

Step-by-step explanation:

Remove the brackets on the right.

y - 7 = 3x + 15

Add 7 to both sides.

y - 7 + 7 = 3x + 15 + 7

y = 3x + 22

The y intercept occurs when x = 0

y = 3*(0) + 22

y = 22