Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.
Let's represent Mrs. West's age as W and her aunt's age as A.
Given that Mrs. West is [tex]14[/tex] years younger than her aunt, we can write the equation:
[tex]W=A-14[/tex]
Also, it's given that Mrs. West's age is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex] . This can be represented as:
[tex]W=60-(A-40)[/tex]
Simplify the equation:
[tex]W=60-A+40\\W=100-A[/tex]
Now, we have two equations for [tex]W[/tex]:
[tex]W=A-14\\W=100-A[/tex]
Since both equations equal [tex]W[/tex], we can set them equal to each other:
[tex]A-14=100-A[/tex]
Now, solve for A:
[tex]A+A=100+14\\2A=114\\A=57[/tex]
Now, plug the value of [tex]A[/tex] into either equation to find [tex]W[/tex]:
[tex]W=57-14\\W=43[/tex]
So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.
COMPLETE QUESTION:
Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], how old is each?
Leticia charges $8 per hour to babysit. She babysat Friday night for 4 hours, and then she babysat again on Saturday. She earned a total of $72. How many hours did Leticia babysit on Saturday? Choose two answers: one for the equation that models this situation and one for the correct answer.
First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. In total, she earned $72. Therefore:
8 ( 4 + x ) = 72
( 4 + x ) = 72 / 8
4 + x = 9
x = 9 - 4
x = 5
Leticia babysat 5 hours on Saturday.
Which of the quadratic functions has the narrowest graph? Y = 1/6x^2, y = 2x^2, y = -x^2, y = 1/8x^2
Answer:
[tex]y=2x^2[/tex]
B is correct
Step-by-step explanation:
Given: We are given equation of parabola ans to choose narrowest graph.
[tex]y=ax^2[/tex]
Parabola form narrowest and widest.
Larger value of a most narrowest graph.
Smaller value of a most widest graph.
Now, we will see the coefficient of x²
[tex]y=\dfrac{1}{6}x^2,\ \ \ a=\dfrac{1}{6}[/tex]
[tex]y=2x^2,\ \ \ a=2[/tex]
[tex]y=-x^2,\ \ \ a=-1[/tex]
[tex]y=\dfrac{1}{8}x^2,\ \ \ a=\dfrac{1}{8}[/tex]
Now, we arrange the value of a in descending order.
[tex]2>1>\dfrac{1}{6}>\dfrac{1}{8}[/tex]
2 is largest value of these.
Hence, The narrowest graph is [tex]y=2x^2[/tex]
The percents of different drinks sold at a snack shop are shown in the circle graph. What percent of the drinks sold were colas?
Write an equation (any form) for the quadratic graphed below
how many liters of a 60% acid solution must be mixed with a 75% acid solution to obtain 20L of a 72% solution
it takes Joanna 15 minutes to complete 4 puzzles. At that rate, how many puzzles can she complete in 1 hour 45 minutes
A certain mixture of nuts contains cashews, almonds, and macadamia nuts. Each container must include three times as many almonds as cashews and twice as many cashews as macadamia nuts. If there are a total of 24 ounces in each container, how many ounces of cashews must be included?
cade road 1 3/5th miles on Saturday and 1 3/4th on Sunday. how far did he ride on the two days?
Which fraction is between 0 and 1/2?
A. 2/3
B. 7/10
C. 3/5
D. 3/8
11. The polygons are similar, but not necessarily drawn to scale. Find the value of a and b.
For which of the inequalities below is v = 4 a solution?
A v + 5 < 8
B v + 5 > 9
C v + 5 ≥ 9
D v + 5 ≤ 8
What is the formula for the surface area of a triangular pyramid
Answer:
4(base*height)/2
Find the equation of the sphere for which the line segment pq connecting p(4,2,1) and q(5,-1,3) is the diameter
Two circles have the same radius. Complete the description for whether the combined area of the two circles is the same as the area of a circle with twice the radius. The combined area of two circles with the same radius is ___πr2. The area of a circle with twice the radius is ___πr2. The combined area of two circles is as the area of a circle with twice the radius.
Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.
A. x = -1 or 15
B. x = 1 or 7
C. x (plus sign over minus sign) square root of 41.
D. x (plus sign over minus sign) square root of 73.
Please help! This is timed!
Answer:
It is D.x=4+√73
Step-by-step explanation:
Got it right on edg.2022 :))
what is 6 ×2/3 in simplest form
Which expression is equivalent to a(^8)^4? a a2 b a4 c a12 d a32
We have been given the expression [tex] (a^8)^4 [/tex].
To solve this problem we will use one of the rules of the exponents called the Power Rule.
The power rule states that:
[tex] (x^m)^n=x^{m\times n}=x^{mn} [/tex]
In our case, x=a and the powers involved are m=8 and n=4.
Therefore, applying the power rule to the case given in our question we get:
[tex] (a^8)^4=a^{8\times 4}=a^{32} [/tex].
Therefore, Option D which says [tex] \boldsymbol{a^{32}} [/tex] is the correct option.
A circle has an area of 75 square centimeters. Which answer is closest to the measure of its radius?
A) 2.75 centimeters
B) 4.9 centimeters
C) 9.8 centimeters
D) 23.9 centimeters
Answer:
4.9
Step-by-step explanation:
Rewrite the equation of the parabola in vertex form. y= x2 + 8x - 21
Answer:
[tex]y=(x+4)^{2}-37[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
if a> 0 then the parabola open upward (vertex is a minimum)
if a< 0 then the parabola open downward (vertex is a maximum)
In this problem we have
[tex]y=x^{2}+8x-21[/tex]
Convert to vertex form
Complete the square
[tex]y+21=x^{2}+8x[/tex]
[tex]y+21+16=(x^{2}+8x+16)[/tex]
[tex]y+37=(x^{2}+8x+16)[/tex]
[tex]y+37=(x+4)^{2}[/tex]
[tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex form
The vertex is the point [tex](-4,-37)[/tex]
the parabola open upward (vertex is a minimum)
Answer:
the answer is y=(x+4)^2-37
Step-by-step explanation:
8,321/100 is equal to which number?
5÷4×6+e=5what does this equal ?
To the nearest hundredth, what is the length of line segment AB ? Drag your answer into the box. The length of line segment AB is approximately units
9.54
10.44
13.00
13.15
Answer:
B. 10.44 units.
Step-by-step explanation:
We are asked to find the length of line segment AB.
To find the length of line segment AB we will use distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Upon substituting the coordinates of point A and B in distance formula we will get,
[tex]\text{Distance between point A and point B}=\sqrt{(1--9)^2+(-1--4)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{(1+9)^2+(-1+4)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{(10)^2+(3)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{100+9}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{109}[/tex]
[tex]\text{Distance between point A and point B}=10.4403065089105502\approx 10.44[/tex]
Therefore, the length of line segment AB is 10.44 units and option B is the correct choice.
Answer:
I'm a nooby so 10.44.
Step-by-step explanation:
for a standard normal distribution whats the probability of getting a positive number
In a standard normal distribution, the probability of getting a positive number is 0.5.
Explanation:Probability of Getting a Positive Number in a Standard Normal Distribution
In a standard normal distribution, the probability of getting a positive number is 0.5. This is because the standard normal distribution is symmetric around 0, and half of the distribution lies to the right of 0, which corresponds to positive numbers.
Evaluate the expression. 12 + 3 • 8
To solve the expression 12 + 3 • 8, first perform the multiplication to get 24, then add this to 12 to get a final result of 36.
Explanation:To evaluate the expression 12 + 3 • 8, you must follow the order of operations, often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. As per PEMDAS, multiplication should be carried out before addition.
First, perform the multiplication: 3 times 8 is 24. Then, add the result to 12.
So, 12 + 24 equals 36. Therefore, the value of the expression 12 + 3 • 8 is 36.
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A pair of vertical angles has measures
(2z+43)°
and
(−10z+25)°
.
What is the value of z? Vertical angles = each other
(2z+43)°
=
(−10z+25)°
−
3
2
−
11
4
−31
Answer:
The answer is Z equals negative 3/2
Step-by-step explanation:
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or .
Since the area of the circle is the area of the square, the volume of the cylinder equals
the volume of the prism or (2r)(h) or πrh.
the volume of the prism or (4r2)(h) or 2πrh.
the volume of the prism or (2r)(h) or r2h.
the volume of the prism or (4r2)(h) or r2h.
The ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
For this case, we're specified that:
Radius of the circle of the cross section of the cylinder = r unitsSide length of the square cross section of the square prism = 2r unitsThen, the area of the circle is:
[tex]\pi r^2 \: \rm unit^2[/tex]
and the area of the square is: [tex]\rm side^2 = (2r)^2= 4r^2 \: \rm unit^2[/tex]
The ratio of the area of the circle to the area of the square is:
[tex]\dfrac{\pi r^2}{4r^2} = \dfrac{\pi}{4} = \pi : 4[/tex]
Thus, the ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4
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A four-sided polygon has sides that measure (2x + 1), (4x – 10), (x + 1)and (12x + 25). What is the perimeter of the polygon, in terms of x?
Final answer:
The perimeter of the polygon, given the sides (2x + 1), (4x – 10), (x + 1), and (12x + 25), is calculated by summing these expressions to get 19x + 17.
Explanation:
To find the perimeter of a four-sided polygon, we add together the lengths of all the sides. Given the sides (2x + 1), (4x – 10), (x + 1), and (12x + 25), the perimeter P in terms of x is calculated by summing these expressions:
P = (2x + 1) + (4x – 10) + (x + 1) + (12x + 25)
Now, we combine like terms:
P = 2x + 4x + x + 12x + 1 – 10 + 1 + 25
P = (2x + 4x + x + 12x) + (1 – 10 + 1 + 25)
P = 19x + 17
Therefore, the perimeter of the polygon in terms of x is 19x + 17.
it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass. how many days does it take 8 goats and 8 cows to eat 17 acres of grass/10929719/ff5df148?utm_source=registration
The 15 days it takes for 8 goats and 8 cows to eat 17 acres of grass if it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass.
Number of days to eat 2 acres for 2 goats and 3 cows = 2/6
Number of days to eat 8 acres for 6 goats and 5 cows = 8/10
Now adding the fraction number of 2/6 and 8/10
[tex]\rm = \frac{2}{6}+ \frac{8}{10}[/tex]
= 68/60
= 15/17
Now the number of days is 15 days for the 17 acres.
Thus, the 15 days it takes for 8 goats and 8 cows to eat 17 acres of grass if it takes 2 goats and 3 cows 6 days to eat 2 acres of grass. it takes 6 goats and 5 cows 10 days to eat 8 acres of grass.
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Which phrase describes the variable expression m + 5?
NEED answer fast, please hurry. If events A and B are independent, and the probability that event A occurs is 83%, what must be true?
The probability that event B occurs is 17%.
The probability that event B occurs is 83%.
The probability that event A occurs, given that event B occurs, is 83%.
The probability that event B occurs, given that event A occurs, is 83%.
Answer:
the answer is C.
Step-by-step explanation:
83%
The true statement about the given conditional Probability is; The probability that event A occurs, given that event B occurs, is 83%.
How to Solve Conditional Probability?
We are told that If events A and B are independent, and the probability that event A occurs is 83%.
Now, Conditional probability like p(A|B) is the probability of event A occurring, given that event B occurs. Thus, applying that to our question means we can denote that;
The probability that event A occurs, given that event B occurs, is 83%.
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