Answer:
265
Step-by-step explanation:
the nth term of an arithmetic progression is given by
[a+(n-1)d]
where "a" is the first term, "d" is the common difference and "n" is the term you're looking for
from the question, a= 17
d=4
n=63
substituting, [17+(63-1)4]=[17+248]=265
The current student population of Memphis is 2900. If the population increases at a rate of 10.7% each year. What will the student population be in 10 years?Write an exponential growth model for the future population P(x) where x is in years:P(x)=What will the population be in 10 years? (Round to nearest student)
Given:
Current population = 2900
rate of increase = 10.7% each year
The exponential growth formula is defined as:
[tex]\begin{gathered} P\text{ = P}_0e^{rt} \\ Where\text{ P}_0\text{ is the initial population} \\ r\text{ is \% growth rate} \\ and\text{ t is time in years} \end{gathered}[/tex]Substituting the given values:
[tex]P(x)\text{ = 2900e}^{0.107x}[/tex]Hence, the exponential model is:
[tex]P(x)\text{ = 2900e}^{0.107x}[/tex]The population in 10 years
We substitute 10 for x in the equation above and solve:
[tex]\begin{gathered} P(x=10)\text{ = 2900e}^{0.107\times10} \\ =\text{ 8454.6005} \\ \approx\text{ 8455 students} \end{gathered}[/tex]Hence, the population of the students after 10 years would be 8455 students
Which equation in standard form has a graph that passes through the point (8,29) and has a slope of 5/2
Answer:
The equation is y = (5/2)x + 9
Step-by-step explanation:
We look for an equation with the form y = mx + b, where m is the slope and b the y-intercept.
We're given the slope, (5/2) which we can use for m:
y = (5/2)x + b
We are told the line goes through (8,29). We need a value of b that will move the line to include this point. Do that by substituting the values:
x = 8, and y=29
y = (5/2)x + b
29 = (5/2)*8 + b
29 = (20) + b
9 = b
The equation is y = (5/2)x + 9
See the attached graph.
can someone please help me figure out what the answer is!!
Answer:
v = 61
Step-by-step explanation:
Hello, of course! These are vertical angles, which means they're equal to each other, so let's set up an equation, shall we? (:
Knowing that they're equal to each other, both sides of the equation should be equal to each other as well, so...
2v + 1 = 123
Now, that we have the equation, we must solve for the variable v!
2v + 1 = 123
- 1 - 1
2v = 122
2v = 122
2 2
v = 61
Therefore, v is 61. Once again, vertical angles are equal to each other, so you set up the equation, where both sides are equal. Hope this helped and best of luck with the rest of your work! <3
The distance from Earth to the sun is approximately 149 million km Taking the speed of light as 3.0 x 10⁸m/s. Calculate how long it takes Sunlight to reach Earth. Give your answer in an appropriate unit
Light takes approximately 8 minutes to reach the earth from Sun.
What is distance?We orbit the Sun at a distance of about 150 million km. Light moves at 300,000 kilometers/second. Divide these and you get 500 seconds, or 8 minutes and 20 seconds. The distance between the Earth's orbit and the Sun's center is between 147 million and 152 million kilometers. Sunlight only needs 490 seconds to reach Earth from its closest point. Finally, it takes 507 seconds for sunlight to reach the farthest location.
Distance = 1.5 x 10^8 km
= 1.5 x 10^11 m
Velocity = 3 x 10^8
Time = (1.5 x 10^11)/(3 x 10^8
= 0.5 x 10^3
= 500 s
= 8 1/3 min
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(HELP PLEASE ASAP) Lydia wants to purchase guitar lessons. She sees a sign that gives the prices for 7 guitar lessons and 11 guitar lessons. Write a linear equation to find the total cost C for d lessons.
Using the slope and y-intercept, the linear function that model this problem is c = 10d + 12
What is Linear FunctionA linear function is a mathematical function that graphs as a straight line. It is a polynomial of degree one and can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
In this problem, we can represent or model the given problem with a set or system of linear equation.
let;
C = cost of lessond = number of lessons.Using y = mx + c and modeling it to suit our given parameter;
m = slope and c = y - intercept
We can take two the two given point and solve for the slope and y - intercept.
m = c₂ - c₁ / d₂ - d₁
m = 122 - 82 / 11 - 7
m = 10
Taking the slope and one point, we can solve for the y - intercept
y = mx + c
82 = 10(7) + c
82 = 70 + c
c = 82 - 70
c = 12
The equation can be written as c = 10d + 12
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pls help A rectangle has a length of 4.3 cm and a perimeter of 14.8 cm. Find the width of the rectangle.
cm
A rectangle has a length of 4.3 cm and a perimeter of 14.8 cm. The width of the rectangle is 3.1 cm.
What is a rectangle?A rectangle is a shape that has four right angles and whose adjacent lengths are not the same.
Given, the length L is 4.3 cm
The perimeter of the rectangle is 14.8 cm.
To calculate the perimeter = 2(l + w)
Putting the values:
14. 8 = 2(4.3) + 2w
Expand the bracket
14. 8 = 8. 6 + 2w
Collect like terms
2w = 14. 8 - 8.6
2w = 6. 2
Divide through by the coefficient of w
w = 6.2/2
w = 3.1 cm
Therefore, the width of the rectangle is 3.1 cm.
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Which point is on the graph of the inverse function h–1(x)?
Solution:
Given:
The graph of the function h(x)
Picking any point on the graph as shown below,
Picking point (0,2) on the graph of the function h(x)
[tex]\begin{gathered} x=0 \\ y=2 \\ \\ \text{Hence, the point of the inverse function is gotten by interchanging the coordinates of the point } \\ ^{}^{} \end{gathered}[/tex][tex]\begin{gathered} \text{If the point of h(x) is }(x,y),thenh^{-1}(x)\text{ is (y,x)} \\ \\ \text{Hence, at (0,2) on h(x)}, \\ h^{-1}(x)\text{ will have the point (2,0)} \\ \\ \text{Also, at (1,0) on h(x),} \\ h^{-1}(x)\text{ will have the point (0,1)} \end{gathered}[/tex]Therefore, a point on the graph of the inverse function of h(x) is (2,0).
Another point on the graph of the inverse function of h(x) is (0,1).
The price that Abigail paid for her snowboard, $77, is less than what Dan paid by $10. How much did Dan pay for his
snowboard?
Find the value of 6f + 7g when f= -3 and g = 2
Pls help thanks
Answer: 6f+7g=6*-3+7*2=-4
Step-by-step explanatiomn]]
Answer:
-4
Step-by-step explanation:
6(-3)+7(2)
-18+14
-4
HELP ASAP
Use what you know about trapezoid properties to solve for x. Confirm the angle measure.
83⁰
X =
Angle (-x +33) =
(-x +33)
degrees.
8 9
10
11
Answer:
the answer is x = -50° and the angle measures 83°
Step-by-step explanation:
in this trapezoid, the angles adiacent to each base have se same amplitude, so:
-x + 33 = 83°. this means the answer is -50 because
-(-50) + 33 = 50 + 33 = 83
7. Here is an inequality: -7- (3x+2) <-8(x + 1)
Select all the values of x that are solutions to the inequality.
A. x = -0.2
B. x = -0.1
C.x=0
D. x = 0.1
E. x = 0.2
F. x = 0.3
(From Unit 2, Lesson 19.)
Answer:
A,B,C,D
Step-by-step explanation:
-7-(3x+2) <=8(x+1)
-7-3x-2<-8x-8
5x<1
x<1/5
x= -0.2, X=-0.1, X=0, X=0.1
The values of x that are solutions to the inequality are C (x = 0) and D (x = 0.1).
Given inequality: -7 - (3x + 2) < -8(x + 1)
Let's solve the inequality step by step:
Distribute the -8 on the right side:
-7 - 3x - 2 < -8x - 8
Combine like terms on both sides:
-9 - 3x < -8x - 8
Add 8x to both sides to isolate the variable terms on one side:
8x - 3x - 9 < -8
Simplify the left side:
5x - 9 < -8
Add 9 to both sides:
5x < 1
Divide both sides by 5 (since 5 is positive, the direction of the inequality does not change):
x < 0.2
Now, let's compare the solutions to the given options:
A. x = -0.2: Not a solution (not less than 0.2)B. x = -0.1: Not a solution (not less than 0.2)C. x = 0: Solution (0 is less than 0.2)D. x = 0.1: Solution (0.1 is less than 0.2)E. x = 0.2: Not a solution (not less than 0.2)F. x = 0.3: Not a solution (not less than 0.2)So, the values of x that are solutions to the inequality are C (x = 0) and D (x = 0.1).
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what is one hundred three thousand thirty three in standard form?
Answer:
103,033
Step-by-step explanation:
Please Help me to answerthe questions and options are in picture
Evelyn has initially $524.96, then she paid $32.50, so she will have less than $500. In order to have at least $500, she needs to deposit the value x.
So the initial value, minus the value paid, plus the deposit needs to be greater than or equal 500, so we have the inequality:
[tex]524.96-32.5+x\ge500[/tex]Solving this inequality for x, we have:
[tex]\begin{gathered} 492.46+x\ge500 \\ x\ge500-492.46 \\ x\ge7.54 \end{gathered}[/tex]Therefore the correct option is the first one (a).
Which expressions are equivalent to the given expression? square root of 40
Answer:
Step-by-step explanation:
√40 = √4*√10
= 2√10 is one equivalent expression
at a certain pizzeria, 1 8 of the pizzas sold in one week were mushroom and 1 3 of the remaining pizzas sold were pepperoni. if n of the pizzas sold were pepperoni, how many were mushroom?
The pizzas sold were (n + 5).
What is the meaning of sold?Past tense and past participle of sales. It is marketed with uncritically related or enthusiastic slang.Sold, for sale. Transfer (goods) to another person or provide (services) for money to another person. Sold to Buyer: He sold me the car for his $1000.If the last sale of the car took place during the talk time or is active, then the statement "This car has been sold 10 times" is correct.But if the last sale of that car happened before the time to speak "Goods Sold" are available. This is passive-past perfect tense means to convince someone that something is good, worthy or useful. Consider the following example:A filmmaker gave me the idea that my book would work on screen.To learn more about sold from the given link :
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922x81=
783x14=
684x15=
650x22=
2525x37=
615x41=
Please help me
Answer:
1. 922x81=74,682
2. 783x14=10,962
3. 684x15=10,260
4. 650x22=14,300
5. 2525x37= 93,425
6. 615x41=25,215
Step-by-step explanation:
at the kennel there are 6 dogs for every five cats
Answer: I have listed each part below
Step-by-step explanation:
a. The ratio of dogs to cats is 6 to 5
b. The ratio of cats to dogs is 5 to 6
c. For every 6 dogs there are 5 cats
d. The ratio of cats to dogs is 5:6
225 words in 5 minutes . what is the unit rate ? at that speed , how many words can be type in 9 minutes
If my grade is an 85 and i make a 67 on an assignment, what is my final grade
The percentage of your grade based on the final grade is 78.8%.
How to calculate the percentage?The information given is incomplete and the complete question is attached below. This was illustrated as "If my grade is an 85 and i make a 67 on an assignment, what is the percentage of my final grade?"
The following can be deduced based on the information illustrated:
Total grade = 85
Your grade = 67
It should be noted that the percentage will be:
= Your grade / Total grade × 100
= 67/85 × 100
= 78.8%
The percentage is 78.8%.
Note that the complete question is given below.
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If my grade is an 85 and i make a 67 on an assignment, what is the percentage of my final grade
Mr. Sloan and Ms. Estrada are teaching their classes how to write in cursive.
Mr. Sloan has already taught his class 3 letters. The students in Ms. Estrada's class, who started the unit earlier, currently
know how to write 5 letters.
Mr. Sloan plans to teach his class 2 new letters per week, and Ms. Estrada intends to cover 1 new letter per week.
Eventually, the students in both classes will know how to write the same number of letters.
At that point, how many letters will the students know?
Graph a line for each class showing the number of letters taught over time and determine the answer by marking the
point of intersection.
When students in both the classes will know how to write the same number of letters, At that point they will know 7 letters
What is point of intersection?
Point of intersection is the point where two lines intersect.
Initially Mr. Sloan has taught his class 3 letters
and Ms. Estrada has taught her class 5 letters.
Now, Mr. Sloan is planning to teach his class 2 letters per week and Ms. Estrada is planning to teach her class 1 letter per week
By this rate after one week Mr. Sloan's class would know 5 letters and Ms. Estrada's class would know 6 letters.
In the second week, Mr. Sloan's class would know 7 letters and Ms. Estrada would know 7 letters.
The graph can be given as below
In the graph the black line represents the letters learned by Mr. Sloan's class and blue line represents the letters learned by Ms. Estrada's class
Also on the x-axis we put the number of weeks and on the y-axis we put the number of letters learned.
Both lines intersect at the coordinate (2,7) Which means that in the second week both the classes would have learned 7 letters
Hence student from both the classes would know 7 letters at the end of 2nd week
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B C С X+19 T S X+29 8. Solve for x. A. 8 B. 9 C.-8 D. -9 Mark for review (Will be highlighted on the review page)
In any triangle, the segment joining the mid-points of two sides is parallel to the third side and equal to half its length
B is the mid-point of RS
C is the mid-point of RT
BC = 1/2 ST
BC = x + 19
ST = x + 29
x + 19 = 0.5(x + 29)
x + 19 = 0.5(x) + 0.5(29)
x + 19 = 0.5x + 14.5
Subtract 0.5x from both sides
x - 0.5x + 19 = 0.5x - 0.5x + 14.5
0.5x + 19 = 14.5
Subtract 19 from both sides
0.5x + 19 - 19 = 14.5 - 19
0.5x = -4.5
Divide both sides by 0.5
[tex]\begin{gathered} \frac{0.5x}{0.5}=-\frac{4.5}{0.5} \\ x=-9 \end{gathered}[/tex]The answer is D
x = -9
2ab-ab+2a+3b+2ab simplified
Answer:
3ab + 2a + 3b
Step-by-step explanation:
Machine A makes 12.75 ounces of popcorn in 3 minutes. Machine B makes 18 ounces of popcorn in 4 minutes.
If each machine makes popcorn for 10 minutes, will there be enough popcorn for eight 9-ounce bags? Explain.
a) Yes; Machine A and Machine B make 77.5 ounces in 10 minutes. 77.5 > 72, so there will be enough popcorn.
b) Yes; Machine A and Machine B make 87.5 ounces in 10 minutes. 87.5 > 72, so there will be enough popcorn.
c) No; Machine A and Machine B make 67.5 ounces in 10 minutes. 67.5 < 72, so there will not be enough popcorn.
d) No; Machine A and Machine B make 30.75 ounces in 10 minutes. 30.75 < 72, so there will not be enough popcorn.
If each machine makes popcorn for 10 minutes, there will be enough popcorn as machine A and machine B make 87.5 ounces in 10 minutes.
According to the question,
We have the following information:
Machine A makes 12.75 ounces of popcorn in 3 minutes.
So, we will find the ounces of popcorn in 1 minute:
3 minutes = 12.75 ounces
1 minute = 12.75/3 ounces
1 minute = 4.25 ounces
So, in 10 minutes machine A will make:
10 minutes = (4.25*10) ounces
10 minutes = 42.5 ounces
Machine B makes 18 ounces of popcorn in 4 minutes.
So, we will find the ounces of popcorn in 1 minute made by machine B:
4 minutes = 18 ounces
1 minute = 18/4 ounces
1 minute = 4.5 ounces
So, in 10 minutes machine B will make:
10 minutes = (4.5*10) ounces
10 minutes = 45 ounces
Now, the total amount of popcorn made by both the machines will be:
Popcorn made by machine A in 10 minutes + Popcorn made by machine B in 10 minutes
42.5 + 45
87.5 ounces
Now, the eight 9-ounce bags mean that there will be 72 ounces of popcorn.
So, we have:
87.5 ounces is greater than 72 ounces.
Hence, the correct option is B.
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what is the answer to [tex]2(10 + n) = 16[/tex]
The initial expression is:
[tex]2(10+n)=16[/tex]So first we can divide by 2 so:
[tex]\begin{gathered} 10+n=\frac{16}{2} \\ 10+n=8 \end{gathered}[/tex]now we rest 10 in bout sides so:
[tex]\begin{gathered} n=8-10 \\ n=-2 \end{gathered}[/tex]what is the simplified value of the exponential expression 33
oa.81
ob.9
oc.18
od.27
The simplified value of the exponential expression 3³ is 27
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Exponent simply mean raising a number to a power. It is also called power or indices. It is given as:
a² = a * a;
a³ = a * a * a
Given the expression:
3³
Applying the law of exponents:
3³ = 3 * 3 * 3 = 27
3³ is 27
The simplified value of the exponential expression 3³ is 27
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2.3.3 congruent triangles
In the congruent triangles both triangle are same . In this triangle 2.3.3 congruent triangle image given below to understand better.
According to the question, given that
2.3.3 congruent triangle under congruence triangle are explain:
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle. We can see from the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and thus P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR.
To be congruent, the two triangles must be the same size and shape. It is necessary for both triangles to be superimposed on one another. A triangle appears to be in a different place or have a different look as we rotate, reflect, and/or translate it.
Two triangles must meet five requirements in order to be congruent. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
SSS Congruence Criteria
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
The three angles of BAC must be identical to the corresponding angles of XYZ if, according to the SSS condition, BAC XYZ.
SAS Congruence Criteria
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
The third side (AB) and the other two angles of ABC must be identical to the equivalent side (XY) and the angles of XYZ if ABC XYZ under the SAS condition.
ASA Congruence Criteria
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
AAS Congruence Criteria
Angle-Angle-Side criterion is also known as the AAS criterion. Two triangles are said to be congruent according to the AAS criterion if any two angles and the non-included side of one triangle match the corresponding angles and side of the second triangle.
RHS Congruence Criteria
Right angle-hypotenuse-side congruence is referred to as the RHS criterion. If the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, then two triangles are said to be congruent according to this criterion.
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Shawn’s coin collection contained quarters, dimes, pennies, and nickels. What was the ratio of quarters to the total number of coins?
A rate ratio two groups' incidence, person-time, or mortality rates. The two groups are often distinguished by demographic traits or by exposure to a suspected causal agent, similar to how the risk ratio distinguishes them.
The jar contains nine quarters, three dimes, and one nickel, for a ratio of nine to three to one. As a result, the ratio of pennies to quarters is 6: 7. c. Sum up the pennies to quarters ratio. The amount of dime coins to all the coins should be written down.
How should a rate ratio be written?
A ratio can be expressed as a fraction 35, 3:5, or with a colon. In contrast, a rate is a comparison of two quantities that may have several units. A rate might be, for instance, 5 miles every 3 hours or 34 dollars per square foot.
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The ingredients list for a homemade lemonade recipe is shown below.
Ingredients:
5 lemons
1 cup of brown sugar
3.5 cups of boiling water
Michael wants to use this recipe, but he only has 3 lemons. How many cups of boiling water should he use with only 3 lemons?
Michael should use 2.1 cups of boiling water with 3 lemons.
We are given the list of ingredients for a homemade lemonade recipe.The ingredients include 5 lemons, 1 cup of brown sugar, and 3.5 cups of boiling water.Michael wants to use the above recipe.He has only 3 lemons to make lemonade according to the recipe.He needs the boiling water in the correct proportions.The ratio of the number of lemons to the number of cups of boiling water in the actual recipe is 5/3.5.Let the number of cups of boiling water required now be "x".The ratio of the available number of lemons to the cups of boiling water is 3/x.The ratio should be the same.5/3.5 = 3/xx = (3*3.5)/5x = 2.1Thus, Michael requires 2.1 cups of boiling water.To learn more about ratios, visit :
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5) How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.
What are perfect square expressions?Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².Square of the subtraction: (a - b)² = a² - 2ab + b².The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.
For the expressions in this problem, we have that:
The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.More can be learned about perfect squares at https://brainly.com/question/14584348
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If the first differences for a table of values is 3.5 the equation is a
equation and the slope is
When first differences are the same it's a linear equation. First differences are equal to the slope, m. General equation is f(x) = mx + b
To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function.
How can one locate an equation?
determine a line's equation from two points:
Using the slope formula, determine the slopeTo find the y-intercept (b), use the slope and one of the points.You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx +b)To learn more about f(x) = mx + b refer to:
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