Answer:
If there are 15 adults we can expect 6 children, for 25 adults we can expect 10 children, and for 40 adults we can expect 16 children.
Write an equation of each line that passes through the following points in slope-intercept form:
M (5, 5) and N (–10, –19)
Help me Please!!!!!
Answer:
[tex]\large\boxed{y=\dfrac{8}{5}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points M(5, 5) and N(-10, -19). Substitute:
[tex]m=\dfrac{-19-5}{-10-5}=\dfrac{-24}{-15}=\dfrac{8}{5}[/tex]
We have the equation:
[tex]y=\dfrac{8}{5}x+b[/tex]
Put the coordinates of the point M to the equation:
[tex]5=\dfrac{8}{5}(5)+b[/tex]
[tex]5=8+b[/tex] subtract 8 from both sides
[tex]-3=b\to b=-3[/tex]
Finally we have the equation:
[tex]y=\dfrac{8}{5}x-3[/tex]
How do Find this answer
Answer:
B and E
Step-by-step explanation:
When the probability of an event is;
Nearing 0, the even is unlikely to happenNeither unlikely nor likely,it is a half, 1/2Nears 1,it is a likely event to happenIn this case event E, with probalility of P(E)=1/2 and event B with probability P(B)=0.49 have the probability neither unlikely nor likely
A coffee shop recently sold 20 drinks, including 8 mochas. Considering this data, how many of the next 95 drinks sold would you expect to be mochas?
Answer:
38 mochas
Step-by-step explanation:
Of the 20 drinks sold, 8 were mochas, so
8/20 = 0.4 = 40% of the drinks they sold were mochas.
If the sold 95 drinks, then 95(0.4) = 38 of them would be mochas if the proportion stays the same
The code to unlock a safety deposit box is three consecutive odd integers whose sum is 75. Find the integers
Answer: The integers are 23, 25, and 27
Step-by-step explanation:
Call the first integer n, and then the next two odd ones are n + 2 and n + 4.
Add them together to get 75:
n + n+ 2 + n + 4 = 75
which becomes 3n + 6 = 75
so 3n = 69, and n is therefore 23. n + 2 = 25, and n + 4 = 27.
The three consecutive odd integers whose sum is 75 are 23, 25, and 27. These are determined by forming an equation with the first odd integer as 'x' and the other two as 'x+2' and 'x+4', respectively, since consecutive odd numbers differ by 2.
The task is to find three consecutive odd integers whose sum is 75. To solve this, we can represent the three consecutive odd integers as x, x + 2, and x + 4. Since the sum of these integers is 75, we can set up the following equation: x + (x + 2) + (x + 4) = 75.
Simplifying the equation we get:
3x + 6 = 75
3x = 69
x = 23
Now we have our first integer x = 23. The next consecutive odd integer would be x + 2 which is 25, and the third one would be x + 4 which is 27. Therefore, the three consecutive odd integers that sum up to 75 are 23, 25, and 27.
Complete the square to determine the maximum or minimum value of the function defined by the expression. x2 + 8x + 6 A) minimum value at 8 B) maximum value at 10 C) minimum value at −14 D) minimum value at −10
Answer:
[tex]\large\boxed{\text{ D) minimum value at -10}}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\ y=x^2+8x+6.\\\\a=1>0,\ \text{the parabola is o}\text{pen up.}\\\text{Therefore the function has the minimum in vertex}\\\\x^2+8x+6=x^2+2(x)(4)+6=x^2+2(x)(4)+4^2-4^2+6\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\to x^2+2(x)(4)+4^2=(x+4)^2\\\\y=(x+4)^2-16+6=(x+4)^2-10\to\text{vertex}\ (-4,\ -10).[/tex]
To determine the minimum value of the quadratic function x^2 + 8x + 6, we complete the square to get the expression (x + 4)^2 - 10 = 0. The function has a minimum value at (x, y) = (-4, -10), so the correct answer is D) minimum value at -10.
Explanation:To find the maximum or minimum value of the quadratic function given by the expression x2 + 8x + 6, we need to complete the square. First, we will write the quadratic in the form of (x + h)2 + k, where h and k are constants.
The coefficient of x is 8. We take half of it, which is 4, and square it to get 16. Now add and subtract this square inside the quadratic expression:
x2 + 8x + 16 - 16 + 6 = 0
Now, group the perfect square trinomial and write it as a square of a binomial:
(x + 4)2 - 10 = 0
To find the minimum value, we set the squared term equal to zero, since the minimum value of a square is zero. As such, (x + 4)2 reaches its minimum value when x = -4, and the overall minimum value of the function is when k = -10. Because this is a quadratic with a positive leading coefficient, the function has a minimum value, not a maximum.
Therefore, the correct answer is D) minimum value at -10.
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The stem and leaf plot below could not represent which of the following
The stem and leaf plot below could not represent "the weight of phonebooks, in pounds".
The stem-and-leaf plot you've provided represents a dataset, but without specific labels for the data points, it's challenging to definitively assign the plot to a particular category. However, we can analyze the options you've provided.
1. **Average number of inches of rain in June:** The data points don't seem to represent rainfall values. Rainfall would typically be measured in fractions or decimals, not whole numbers like 33.
2. **Height of plant seedlings, in inches:** This is a possibility, especially if the numbers represent the height of seedlings in inches. The decimal point represented by the key (3 | 5 means 3.5) supports this interpretation, indicating a measurement in inches.
3. **Weight of phonebooks, in pounds:** Phonebook weights are usually measured in pounds or ounces. The given numbers do not correspond to common weights and are unlikely to represent phonebook weights.
4. **Height of NBA basketball players, in meters:** NBA player heights are typically measured in feet and inches, not meters. Additionally, the provided numbers do not align with typical heights of NBA players.
Given the context of the data and the presence of the decimal point in the key, it's most likely that the stem-and-leaf plot represents the **height of plant seedlings, in inches.** This interpretation is consistent with the format of the data and the provided key, suggesting measurements in inches.
So, the correct answer is "the weight of phonebooks, in pounds".
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Samantha is painting the outside of a box that is in the shape of a rectangular prism. It’s length is 18cm, it’s width is 6 cm, and it’s height is 3cm. What is the surface area of the box in square cm?
A. 162 cm squared
B. 180 cm squared
C. 324 cm squared
D. 360 cm squared
D. 360 cm squared
Explanation:
Multiply each faces edges.
18x7(WxL)
3x6(HxW)
3x18(HxL)
multiply each equations answer by 2, because the opposite face is the same.
108x2=216
18x2=36
54x2=108
add these together to get 360 cm squared.
The surface area of the box is 360 cm².
Explanation:To find the surface area of the rectangular prism, we need to find the areas of all the sides and add them together.
The formula to find the surface area is:
Surface Area = 2lw + 2lh + 2wh
Plugging in the given dimensions:
Surface Area = 2(18)(6) + 2(18)(3) + 2(6)(3) = 216 + 108 + 36 = 360 cm²
Therefore, the surface area of the box is 360 cm², which is option D.
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Find the least common denominator of 3/20 and 9/8
Answer:
40
Step-by-step explanation:
To find the least common denominator, you find the least common multiples of the denominators, which in this case is 20 and 8.
Tower method:
Start: |20, 8
4 |20, 8 -> 4 is a factor that 20 and 8 have in common
5, 2 -> 20/4 = 5, 8/4 = 2, those numbers do not have a common factor.
4 * 5 * 2 = 40.
The fractions with 40 as its denominator is 6/40 and 45/40.
The larger of two number is 5 more than the smaller. The smaller number plus the twice the larger equals 100. Find the numbers
Answer:
smaller number :30
larger number : 35
Step-by-step explanation:
Enter the missing numbers in the boxes to complete the table of equivalent ratios of lengths to widths. PLS HELP WORTH 50 POINTS!!!!!
Length (cm) Width (cm)
6 ?
9 36
? 48
15 ?
i think they were multiplying each by 4. so 6x4 would be 24. and 12x4 = 48, then 15x4= 60. so i believe the blanks are 24,12,60.
Answer:
x y
6 24
9 36
12 48
15 60
Step-by-step explanation:
We need to find the rate of change in the table.
Lets start with the x-values.
6 to 9?
9 - 6 = 3
So, the rate of change in the x-value is 3
9 to 3 is 12
12 to 3 is 15
Now let's go onto the y-values.
We don't know the first number, so let's move to the next number, 36.
36 to 48?
48 - 36 = 12
Therefore, the rate of change in the y-value is 12
So, let's work backwards to find the first number.
36 - 12 = 24
48 + 12 = 60
Another easier way you could do it (really simple).
9 times what is 36?
9 x 4 = 36, right?
So, the change of rate is 4
So multiply everything in the x column by 4.
6 x 4 = 24
15 x 4 = 60
Since we don't have one the x value for 48, divide it by 4 which is 12
Voilà ;)
Gabriella uses 8.4 pints of white paint and blue paint to paint her bedroom walls.
2/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:
8
Step-by-step explanation:
covert 8.4 into a fraction which would be 42/5
then subtract 42/5 from 2/5 and youll get 8
Final answer:
To calculate the amount of blue paint Gabriella used, multiply 8.4 pints by 2/5 to determine the white paint, and then subtract this from the total, resulting in 5.04 pints of blue paint.
Explanation:
Gabriella uses a total of 8.4 pints of paint to paint her bedroom walls, with 2/5 of this amount being white paint. To find out how many pints of blue paint she used, we first need to determine the amount of white paint and then subtract that from the total.
Multiply the total amount of paint by 2/5 to find the white paint: 8.4 pints imes 2/5 = 3.36 pints (white paint).
To find the blue paint, subtract the white paint from the total paint: 8.4 pints - 3.36 pints = 5.04 pints (blue paint).
Therefore, Gabriella used 5.04 pints of blue paint to paint her bedroom walls.
Order from least to greatest 0.14,1/8,1.9%
Answer: 1/8,1.9,0.14
Step-by-step explanation:
Answer:
0.019 (1.9%), 0.14, 0.125 (1/8)
Step-by-step explanation:
Write the letter of the largest number (below): _____
A. 0.9837 B. 2/165 C. 4 x 10-5 D. 23
Answer:
C.
Step-by-step explanation:
4x10 = 40 - 5 = 35.
35 is bigger than 23,
35 is bigger than 0.9837
and 35 is also bigger than 2/165, therefore 35 is the largest number.
factor completely. x^2+4x-12
Answer:
(x + 6)(x - 2)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term ( + 4)
The factors are + 6 and - 2 since
+ 6 × - 2 = - 12 and + 6 - 2 = + 4, hence
x² + 4x - 12 = (x + 6)(x - 2)
simplify b^10/b^2, help me pls
Answer:
[tex]\text{\bf{A.}}\quad b^8[/tex]
Step-by-step explanation:
It may be helpful to remember that an exponent signifies repeated multiplication:
b¹⁰ = b·b·b·b·b·b·b·b·b·b . . . . . . . b is a factor 10 times
and
b² = b·b . . . . . . . . . . . . . . . . . . . . b is a factor 2 times
Then the division can be simplified by using the denominator factors to cancel 2 of the numerator factors:
[tex]\dfrac{b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b}{b\cdot b}=b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b=b^8[/tex]
In terms of exponents, we write this as ...
[tex]\dfrac{b^{10}}{b^2}=b^{10-2}=b^8[/tex]
Answer:
A) b^8
Step-by-step explanation:
At the airport, ten people are waiting on standby. Two seats become available, one first class and one coach. How many ways are there to fill the two seats?
10
20
45
90
Answer:
Last Option
Step-by-step explanation:
We have 10 people and two seats. Then we must choose 2 people out of 10 to occupy the seats.
The seats are different so the order in which people feel is important.
This is a problem of permutations
For the first seat I must choose a person of between 10.
For the second seat I must choose a person from 9.
So, if we call m the number of ways in which you can assign the seats:
[tex]m = 10*9\\\\m = 90[/tex]
Answer:
90
Step-by-step explanation:
The back of mangled angles
Answer:
what do you want me to do?
Step-by-step explanation:
help please!!! thank u!
Answer:
99
Step-by-step explanation:
The perimeter is increased by a factor of 3. The formula for perimeter is
New Perimeter = scale factor * original perimeter.
Area is a different matter. It is
New area = (scale factor)^2 * old area
Givens
old area = 11
Solution
New Area = 3^2 * 11
New area = 9 * 11
New area = 99
solve -37 + n equals -56 for n
Simplifying
-37 + n = -56
Solving
-37 + n = -56
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '37' to each side of the equation.
-37 + 37 + n = -56 + 37
Combine like terms: -37 + 37 = 0
0 + n = -56 + 37
n = -56 + 37
Combine like terms: -56 + 37 = -19
n = -19
Simplifying
n = -19
Answer:
N=-19
Step-by-step explanation:
Just add 37 to bot sides
What is the length of the intercepted arc?
First you need to calculate the circumference of the circle:
Circumference = diameter x PI = 16 x PI = 16 * 3.14 = 50.24
The intercepted arc is 15 degrees.
To find the length multiply the circumference by the central angle divided by 360.
Arc length = 50.25 x (15/360) = 2.1 units.
If a certain number is added to the numerator and denominator of 8/11, the result is 6/7. Find the number.
Answer:
x = 10
Step-by-step explanation:
8 + x = 6
11 + x 7
Cross Multiply
6(11 + x) = 7(8 + x)
66 + 6x = 56 + 7x
10 = x
The number that needs to be added to the numerator and denominator of 8/11 to result in 6/7 is 10.
Explanation:The subject of the question is Mathematics, specifically algebra and fractions. We can represent the student's problem with an equation, where x stands for the unknown number to be added to the numerator and denominator of 8/11 to get 6/7.
The initial fraction is 8/11 and the desired fraction is 6/7. Hence, we can translate this problem into the equation: (8 + x)/(11 + x) = 6/7. By cross-multiplying to eliminate the fractions, we get: 7(8 + x) = 6(11 + x). Simplified, this equation becomes 56 + 7x = 66 + 6x. Solving for x, we subtract 6x from both sides: x = 66 - 56, so x = 10.
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help plz explain how to do this.
Answer:
1/3
Step-by-step explanation:
Select all expressions that are equivalent to -36x+54y-90
The equivalent expressions of -36x+54y-90 are -18(2x - 3y + 5), 18(-2x + 3y - 5), and -2(18x - 27y + 45). So options (2), (4) and (5) are correct.
To determine which expressions are equivalent to -36x + 54y - 90, we'll distribute the coefficients and compare the resulting expressions.
Let's start by distributing each expression:
1. -9(4x - 6y - 10) = -36x + 54y + 90
2. -18(2x - 3y + 5) = -36x + 54y - 90
3. -6(6x + 9y - 15) = -36x - 54y + 90
4. 18(-2x + 3y - 5) = -36x + 54y - 90
5. -2(18x - 27y + 45) = -36x + 54y - 90
6. 2(-18x + 54y - 90) = -36x + 108y - 180
Among these, expressions 2, 4, and 5 result in the same expression as -36x + 54y - 90.
Expression 2 is -18(2x - 3y + 5), expression 4 is 18(-2x + 3y - 5), and expression 5 is -2(18x - 27y + 45).
Therefore, the equivalent expressions are -18(2x - 3y + 5), 18(-2x + 3y - 5), and -2(18x - 27y + 45).
____ improves as degree of educational attainment increases.
A)Interest rate
B)median income
C)savings ability
D)borrowing rate
Median income improves as degree of educational attainment increases. (B)
The answer is B) median income
Rachel likes to read books. She records the number of books she read over a period of 5 weeks. The set of ordered pairs below gives the details, where the x-coordinate is the number of weeks since she starts recording and the y-coordinate is the number of books she read each week.
Which of the following describes the set of ordered pairs?
A. both a relation and a function
B. a function only
C. neither a function nor a relation
D. a relation only
Answer:
A. both a relation and a function
Step-by-step explanation:
The given set of ordered pairs is
{(1,2),(2,3),(3,1),(4,4),(5,2)}.
This ordered pairs represent a relation.
The x-coordinates represent the domain and the co-domain or range is the set of the y-coordinates.
The relation is many-to-one relation.
All many-to-one relations are functions.
The correct choice is A.
????????????????????
Answer:
A= 28-16x B+= 21y
Step-by-step explanation:
For A you use distributive properties to get your answer and for B since they all have the same variable you can add them like regular addition.
What are the possible outcomes of randomly choosing one of the tiles shown?
The possibility of randomly choosing one of the tiles is 1/9
What is the surface area of this rectangular prism? 10 Points to the right answer! :D
Answer:
[tex]S.A=160cm^2[/tex]
Step-by-step explanation:
The surface area of a rectangular prism is given by the formula;
[tex]S.A=2(lw+lh+wh)[/tex]
From the diagram;
The length is [tex]l=10cm[/tex].
The width is [tex]w=5cm[/tex].
The height is [tex]h=2cm[/tex].
Substitute these values into the formula to obtain;
[tex]S.A=2(10\times5+10\times2+5\times2)[/tex]
[tex]S.A=2(50+20+10)[/tex]
[tex]S.A=2(80)[/tex]
[tex]S.A=160cm^2[/tex]
What is the solution to the inequality -4x < 8? x < -24 x > -24 x < -2 x > -2
Answer:
x > -2
Step-by-step explanation:
Solve the inequality -4x < 8 using inverse operations. If you divide or multiply by a negative, flip the inequality sign.
[tex]-4x < 8\\\\\frac{-4x}{-4} < \frac{8}{-4}[/tex]
x > -2
can someone help me with this?
Answer:
780Step-by-step explanation:
What is the sum of the series 5^n from n=1 to 4.
5^1 + 5^2 + 5^3+ 5^4 =
5 + 25 + 125 + 625 =780