To find the number that, when added to 1/2, equals 7/8, you must subtract 1/2 from 7/8. The solution to this problem is 3/8, meaning that 1/2 plus 3/8 equals 7/8.
Explanation:To solve the problem 1/2 plus what equals 7/8, you need to subtract 1/2 from 7/8. This is because you want to find out what number added to 1/2 will give you 7/8. Here is the step-by-step solution:
Convert 1/2 and 7/8 into decimal form. This would be 0.5 and 0.875, respectively. Then subtract 0.5 (which is 1/2) from 0.875 (which is 7/8). This results in 0.375. Then, convert 0.375 back into a fraction. The decimal 0.375 is equal to the fraction 3/8.So, 1/2 plus 3/8 equals 7/8.
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Final answer:
To find the number that when added to 1/2 equals 7/8, convert 1/2 to 4/8 so both fractions have a common denominator. Subtract 4/8 from 7/8, resulting in 3/8. Thus, 1/2 plus 3/8 equals 7/8.
Explanation:
The student is asking us to find the number that, when added to 1/2, equals 7/8. To solve this, we need to find a common denominator, which is 8 in this case. For 1/2, we multiply the numerator and denominator by 4 to convert it to 4/8. Now we have a common denominator, so we can find the missing number.
7/8 - 4/8 = 3/8
Therefore, 1/2 plus 3/8 equals 7/8. This calculation is based on the intuition that a number is needed to bridge the gap between 4/8 and 7/8.
A vertical flagpole is attached to the top edge of a building. A man stands 400 feet from the base of the building. From his viewpoint, the angle of elevation to the bottom of the flagpole is 60°, to the top is 62.5°. Determine the height of the flagpole.
Answer: The flagpole is 75.6 feet (approximately)
Step-by-step explanation: Please refer to the picture attached.
The man is at point C and the base of the building is point B, and he looks up at an angle of elevation of 60 degrees to the bottom of the flagpole. Note that the flagpole is attached to the top of the edge of the building which is point A. Also he looks up at an angle of elevation of 62.5 degrees to the top of the flagpole which is point A.
If his distance from the base of the building is 400 feet (line BC), then we would start by calculating the height of the building plus the flagpole (line FB) and then the height of the building itself (line AB) and the difference between both would be the height of the flagpole (line FA).
We shall use the trigonometric ratios as follows;
In triangle FBC,
Tan C = opposite/adjacent
Tan 62.5 = FB/400
Tan 62.5 x 400 = FB
1.9209 x 400 = FB
768.36 = FB
Also in triangle ABC,
Tan C = opposite/adjacent
Tan 60 = AB/400
Tan 60 x 400 = AB
1.732 x 400 = AB
692.8 = AB
The height of the vertical flagpole can be derived as
FA = FB - AB
FA = 768.36 - 692.8
FA = 75.56
FA ≈ 75.6
Therefore the height of the flagpole is 75.6 feet (approximately)
The height of the flagpole is required to be found with the given angles of elevation.
The height of the flagpole is 75.6 feet.
From trigonometric ratios
[tex]\tan60=\dfrac{BD}{BC}\\\Rightarrow BD=BC\tan60\\\Rightarrow BD=400\tan60[/tex]
[tex]\tan62.5=\dfrac{AB}{BC}\\\Rightarrow AB=BC\tan62.5\\\Rightarrow AB=400\tan62.5[/tex]
So,
[tex]AD=AB-BD\\\Rightarrow AD=400(\tan62.5-\tan60)\\\Rightarrow AD=75.6\ \text{feet}[/tex]
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Plz hurry
The mean of a data set is 30. What is the deviation from the mean of a data point 27 that was part of the data set?
a) 1.5
b) –3
c) 3
d) –1.5
Answer:
c
Step-by-step explanation:
The deviation from the mean for the data point 27 in a data set with mean 30 is -3.
Explanation:In mathematics, the deviation from the mean of a data set is a measure of the distance between each data point and the mean. It is obtained by subtracting the mean from the data point. In this case, the mean of the data set is given as 30. To find the deviation from the mean for the data point 27, you simply subtract 30 (the mean) from 27 (the data point).
So 27 - 30 = -3
This means the deviation from the mean for the data point 27 is -3 which corresponds to option b.
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Central angle ACD of circle C has a measure of 50 degrees. What is the measure of arc AD? What is the measure of inscribed angle ABD?
Please help!
Answer:
see explanation
Step-by-step explanation:
The inscribed angle ABD is on half the central angle ACD, that is
∠ ABD = 0. × 50° = 25°
The measure of arc AD is equal to the central angle it subtends, thus
arc AD = 50°
1. The measure of inscribed angle [tex]\( \angle ABD \)[/tex] is 25 degrees. 2. The measure of arc [tex]\( AD \)[/tex] is 50 degrees.
To solve this problem, we need to understand the relationship between central angles, arcs, and inscribed angles in a circle.
1. Measure of Arc AD:
The measure of an arc created by a central angle in a circle is equal to the measure of the central angle itself. Given that the central angle [tex]\( \angle ACD \)[/tex] is 50 degrees, the measure of arc [tex]\( AD \)[/tex] is also 50 degrees.
[tex]\[ \text{Measure of arc } AD = 50^\circ \][/tex]
2. Measure of Inscribed Angle ABD:
An inscribed angle that intercepts the same arc as a central angle will have a measure that is half the measure of the central angle. In this case, the inscribed angle [tex]\( \angle ABD \)[/tex] intercepts arc [tex]\( AD \)[/tex], which has a measure of 50 degrees.
[tex]\[ \text{Measure of } \angle ABD = \frac{1}{2} \times \text{Measure of arc } AD = \frac{1}{2} \times 50^\circ = 25^\circ \][/tex]
The complete question is:
Central angle ACD of circle C has a measure of 50 degrees. What is the measure of arc AD? What is the measure of inscribed angle ABD?
1. [tex]\( \angle ABD \)[/tex] = ______.
2. arc [tex]\( AD \)[/tex] = ______.
Ok so can someone pls help me on this. It’s math, and pls explain.
Answer:
3)a. (80 km/hour)(6 hours) = 480 km
b. 480 km/5 hours = 96 km/hour
Determine the solution?
Answer:
c) (-∞, -4] or [7,∞)
Step-by-step explanation:
x² - 3x - 28 ≥ 0
x² - 7x + 4x -28 ≥ 0
x (x - 7) + 4(x - 7) ≥ 0
(x-7) (x + 4) ≥ 0
When x value lies in (-∞, -4], (x-7) value will be negative and (x+ 4) will be negative. So, result will be positive
When x value lies in [7,∞), both (x-7) and (x+ 4) will be positive. So, result will be positive
Raj was asked to fully simplify this polynomial and put it into standard form.
2x+y + 8x? – xy2 - 2x + 3xy2 + 6y?
Raj simplified the polynomial with a final term of 6y. What is the first term of the polynomial Raj ended up with?
6x?
Box
2xy?
Answer: 16y- 2xy
Step-by-step explanation:
11. A box of apples has a mass of 17.5 kg.)
A box of pears has a mass of 15.5 kg.
a) Write an algebraic expression for the
total mass of a boxes of apples and
p boxes of pears.
b) Use your expression to determine the
total mass of a shipment of 32 boxes of
apples and 41 boxes of pears.
a) 17.5a + 15.5p = t
b) Total mass of the shipment is 1195.5kg
Step-by-step explanation:
Mass of 1 box of apple= 17.5kg
Mass of 1 box of pears = 15.5kg
a) expression for getting total mass:
Let the no. of boxes of apple be 'a'
Let the no. of boxes of pears be 'p'
Let the total mass be 't'
17.5a + 15.5p = t
b) a = 32
p = 41
17.5a + 15.5p = t
17.5(32) + 15.5(41) = t
560 + 635.5 =t
1195.5 = t
Total mass of the shipment is 1195.5kg
Please help me, i've asked before but go no answer. Brainliest to correct answer and thanks to all answers
Answer:
The answer is B.
Step-by-step explanation:
All other answers are irrational
Question in Image. Thanks!
what is the slope of y= -1+3x
Step-by-step explanation:
Slope of this equation is 3
Answer:
Slope = 3
Step-by-step explanation:
[tex]y = - 1 + 3x \\ y = 3x - 1 \\ equating \: it \: with \\ y = mx + b \\ \huge \red{ \boxed{slope \: (m) = 3 }}\\ [/tex]
A circular lawn of radius 10 mhas a circular flower bed of radius 5m dug into it.
What is the area of the remaining lawn? Give your answer in terms of pi (3.14)
Answer:
75π [tex]m^{2}[/tex] ≈ 235.62 [tex]m^{2}[/tex]
Step-by-step explanation:
R represents the radius of the lawn
r represents the area of the circular bed
So,
Area of the remaining lawn, A = area of the lawn - area of the circular flower bed
A = πR^2 - π^2
A = π(R^2 - r^2)
A = π(10^2 - 5^2)
A = π( 100 - 25)
A = 75π [tex]m^{2}[/tex] ≈ 235.62[tex]m^{2}[/tex]
Determine the slope of the line below.
A. -3/2
B. 2/3
C. 3/2
D. -2/3
Answer:
B
Step-by-step explanation:
Count from the y-intercept to the next natural point. 2 up and then 3 across
If x = 12 cm, what is the volume of the prism?
7 cm³
Answer:
84
Step-by-step explanation:
Which of the following points lies on the graph of this equation?
A) (-3,2)
B) (3,5)
C) (3,3)
D) (6,8)
Answer:
C(3,3)
Step-by-step explanation:
Help please?
What are the factors of the product represented below?
Answer:
B
Step-by-step explanation:
count how many x^2 there are because they would tell you what your answer is.
Answer: Its B.
Step-by-step explanation:
Ther are 6 x2. So it is (6x2+2x)
There are also 6 Xs so it's (6x+2)
Solve the equation.
5x + 6 = 2(2x – 3)
x =
How do you do question 3?
Answer:
Standard Form: 4x-1x^3-5x^2.
Answer:
[tex]4x + {x}^{3} - 5 {x}^{2} [/tex]
Step-by-step explanation:
[tex]4x - 3 {x}^{3} + 2 {x}^{3} - 5 {x}^{2} \\ = 4x + {x}^{3} - 5 {x}^{2} [/tex]
Latisha determined the approximate amount of time each student in her homeroom class spent outside on a sunny day and on a rainy day. The dot plots below show her results.
Sunny Day
A dot plot titled Sunny Day. A number line going from 35 to 90 is labeled Minutes Spent Outside. There are 0 dots above 35, 1 above 40, 2 above 45, 2 above 50, 3 above 55, 2 above 60, 2 above 65, 2 above 70, 1 above 75, and 0 above 80 and 90.
Cloudy Day
A dot plot titled Cloudy Day. A number line going from 35 to 90 is labeled Minutes Spent Outside. There is 1 dot above 35, 4 above 40, 5 above 45, 3 above 50, 2 above 55, and 0 above 60, 65, 70, 75, 80, and 90.
Which measures of center and variability can be used to most accurately compare the two data sets?
mean and MAD
mean and IQR
median and MAD
median and IQR
Answer:
THE ANSWER IS A. I HAD THE SAME QUESTION
Step-by-step explanation:
Answer:
I think its A
Step-by-step explanation:
Iris charges $50 for her consulting services plus $60 for each hour she
works. On one job, Iris charged $470. Write and solve an equation to
model this scenario. Use the variable h
O
50 + 60h = 470
0
50h + 60 = 470
0
60h + 470 = 50
50h + 470 = 60
Answer:
50+60h = 470
Step-by-step explanation:
50 is the constant as she charges a base fee.
"For each" => price varies => "varies" => variable => x
50+60h = 470.
Given the function g(x) = x^2+ 10x + 23, determine the average rate of change of
the function over the interval -8 < X < -4.
The average rate of change of the function g(x) = x^2 + 10x + 23 over the interval -8 < x < -4 is -0.5.
Explanation:To determine the average rate of change for the function g(x) = x^2 + 10x + 23 over the interval -8 < x < -4, we first plug these x-values into the function to find the corresponding y-values:
G(-8) = (-8)^2+ 10*(-8) + 23 = 9
G(-4) = (-4)^2+ 10*(-4) + 23 = 7.
The average rate of change will then be the change in y-values divided by the change in x-values, so:
Average Rate of Change = [G(-4) - G(-8)]/[-4 - (-8)] = (7 - 9)/(-4 - (-8)) = -2/4 = -0.5.
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A line has a slope of Negative one-half and a y-intercept of –2. A coordinate plane. What is the x-intercept of the line?
In a coordinate plane, the x-intercept of the line x + 2y + 4 = 0 will be (–4, 0).
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
A line has a slope of Negative one-half and a y-intercept of –2.
m = – 1/2
c = – 2
The equation of line will be
y = –(1/2)x – 2
1/2x + y + 2 = 0
x + 2y + 4 = 0
For the x-intercept, the value of y will be zero.
x + 2y + 4 = 0
Put x = 0, then the value of y will be
x + 2(0) + 4 = 0
x + 4 = 0
x = –4
Then the x-intercept of the line x + 2y + 4 = 0 will be (–4, 0).
The equation of the line is drawn in the graph.
It can be clearly observed the line intersect at (-4, 0) and (0, -2).
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Answer:
-4 is the answer
Step-by-step explanation:
QuesLUI OUI 15
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You scored a 95% on your math quiz. The quiz was out of 60 points. How many points did you get?
Answer:
55
Step-by-step explanation:
You got 57 points on your math quiz.
To find out how many points you got on the math quiz, we need to calculate 95% of the total points the quiz was out of. The quiz was out of 60 points.
First, we convert the percentage score to a decimal by dividing by 100:
[tex]\[ 95\% = \frac{95}{100} = 0.95 \][/tex]
Next, we multiply the decimal score by the total points to find out the number of points obtained:
[tex]\[ 0.95 \times 60 = 57 \][/tex]
So, you got 57 points on your math quiz.
324.8 rounded to the nearest ten
Answer:
Step-by-step explanation:
so you take the eight and round it so then it makes a zero and the 4 becomes a 5
Answer:
320
Step-by-step explanation:
320
As your rounding to the ten place if your number is above five you round up if its below you round down.
If the surgeon and the pharmacist each worked 30 years, how much more money does the surgeon make in lifetime income?
Answer:
3,467,700 excluding years studying
Step-by-step explanation:
Every year the Surgeon makes $115,590 more than the Pharmacist (230,540-114,950)
$115,590 * 30 = $3,467,700
The surgeon makes $9,900,000 more in lifetime income than the pharmacist over a working period of 30 years.
To answer the question about how much more money a surgeon makes in lifetime income compared to a pharmacist, we first need to understand the potential earnings of both professions over a 30-year working period.
Step 1: Define Earnings for Each Profession
Let's assume:
The surgeon earns an average of $450,000 per year.The pharmacist earns an average of $120,000 per year.Step 2: Calculate Lifetime Income
For the Surgeon:
Lifetime income = Annual salary × Number of years workedLifetime income = $450,000 × 30 = $13,500,000For the Pharmacist:
Lifetime income = Annual salary × Number of years workedLifetime income = $120,000 × 30 = $3,600,000Step 3: Calculate the Difference in Lifetime Income
To find out how much more the surgeon makes compared to the pharmacist, we subtract the pharmacist's total income from the surgeon's total income:
Difference = Surgeon’s income - Pharmacist’s incomeDifference = $13,500,000 - $3,600,000 = $9,900,000Conclusion
In conclusion, the surgeon makes $9,900,000 more in lifetime income than the pharmacist over a working period of 30 years.
State the type of trinomial, and factor: y2 + 8y + 16.
A. regular trinomial; (y + 2)(y + 8)
B. regular trinomial; (y – 2)(y – 8)
C. perfect square trinomial; (y + 4)2
D. perfect square trinomial; (y + 8)2
Answer: Option C
We will factor 16 so that the sum of the factors is 8.
Such factors are 4 and 4.
So the factorization of the given expression is:
[tex]y^2+8y+16\\=y^2+4y+4y+16\\=y(y+4)+4(y+4)\\=(y+4)(y+4)\\=(y+4)^2[/tex]
So the given trinomial is a perfect square trinomial.
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The circumference of a circle is 36x feet. What is the length of the radius of this circle?
O oft
O 18h
O 36 ft
O 72 ft
Answer:
18h
Step-by-step explanation:
if Anthony has twice as nickels as one and one has 15 more nickels than Maria what is the value in dollars of Anthony's Nickels if Maria has six Nickels
Explain?
Answer:
Anthony has $2.10
Step-by-step explanation:
If Maria has 6 nickels and one has 15 more nickels than Maria, one has a total of 21 nickels. Since Anthony has twice the amount of nickels as One, you would multiply 21 by 2 to get a total of 42. It takes 20 nickels to make a dollar. If you divide 42 by 20 you get 2.1, which is equivaldnt to $2.10
What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(x + 5)? A) translate vertically 5 units up B) translate vertically 5 units down C) translate horizontally 5 units left D) translate horizontally 5 units right
Answer:
C) translate horizontally 5 units left
Step-by-step explanation:
f(x + 5)
Is a change in domain
The graph of f(x) is shifted 5 units towards the left to obtain the graph of f(x+5)
Answer:
C
Step-by-step explanation:
When we only change the x part of the function (that is, we add, subtract, multiply, or divide something in relation to the x part of f(x)), that is called a horizontal transformation. When we change the entire function, that's a vertical transformation.
In this case, because we are only changing the x (we turn f(x) into f(x + 5)), this is a horizontal transformation. One thing to note about horizontal transformations is that they are "backwards", which means that if we add to the x, we actually move the graph in the negative direction (which is to the left), whereas if we subtract from x, we move the graph in the positive direction (which is to the right).
Here, we're adding 5 to x, which we know means that we are translating the graph of f(x) horizontally to the left 5 units.
Thus, the answer is C.
Hope this helps!
A regular hexagon is shown.
A rectangular hexagon has an apothem with length 12 inches and a radius with length c. The apothem cuts the side of the hexagon into 2 equal parts with length b.
What is the measure of the radius, c, rounded to the nearest inch? Use the appropriate trigonometric ratio to solve.
6 in.
10 in.
14 in.
24 in.
Answer:
The answer is C) 14in.
Step-by-step explanation:
this is very easy, you just gotta do this, then that, then this, blablablabla you will get 100%
The radius of the hexagon with an apothem of 12 in is 14 inches.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
The angles of a hexagon measure 60 degrees each, since it is bisected, the angle becomes 30 degrees.
Let c represent the radius of the hexagon, hence:
cos(30) = 12/c
c = 14 in
The radius of the hexagon with an apothem of 12 in is 14 inches.
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Can someone please answer this with a real answer? all I've been getting is fake answers for the points. I need this to pass!!
Some studies find that the yearly growth rate of a certain wildflower can be modeled by the equation Y=1000(1.08)^x. Use the properties of exponents to show an equivalent equation that represents the monthly growth of the wildflowers. Find the values of a, b, c, and d. Round to the nearest thousandth as needed.
y=1,000(1.08)x
=1,000((1.08)1/a)^bx
a=
b=
=1,000(c)^dx
c=
d=
Final answer:
To find the equivalent equation for the monthly growth of the wildflowers, we need to convert the yearly growth rate to a monthly growth rate. The monthly growth rate is the 12th root of the yearly growth rate. The equivalent equation is Y=1000((1.08)^(1/12))^mx.
Explanation:
To find an equivalent equation that represents the monthly growth of the wildflowers, we need to convert the yearly growth rate into a monthly growth rate. Since there are 12 months in a year, the monthly growth rate is the 12th root of the yearly growth rate.
Given the equation Y = 1000(1.08)^x, where x represents the number of years, the equivalent equation for the monthly growth rate is Y = 1000((1.08)^(1/12))^mx.
Here, a = 12, b = 1/12, c = 1.08, and d = m.
The value we get are :
a = 1000
b = 1.00692
c = 0
d = 0
The given equation, Y=1000(1.08)^x, represents the yearly growth of wildflowers, where:
Y is the number of wildflowers in year x.
1000 is the initial number of wildflowers (at year x=0).
1.08 represents the yearly growth factor (8% increase).
x is the year number.
To find the equivalent equation for monthly growth, we need to consider that there are 12 months in a year. This means the yearly growth factor can be further divided into monthly growth factors.
Divide the exponent by the number of months:
In the yearly equation, the exponent x represents the year number. To represent months, we need to divide x by 12 (number of months in a year).
The new equation becomes: Y = 1000 * (1.08)^(x/12).
Apply the power of a power property:
(a^b)^c = a^(b*c). In this case, a = 1.08, b = 1/12, and c = x.
The equation becomes: Y = 1000 * ((1.08)^(1/12))^x.
Simplify the equation:
Calculate (1.08)^(1/12) using a calculator. This value is approximately 1.00692 (rounded to nearest thousandth).
Substitute this value back into the equation: Y = 1000 * (1.00692)^x.
Therefore, the equivalent equation representing the monthly growth of wildflowers is:
Y = 1000 * (1.00692)^x
Values of a, b, c, and d:
a = 1000 (initial number of wildflowers)
b = 1.00692 (monthly growth factor)
c = 0 (no x term in the exponent)
d = 0 (no constant term)
Question:
Some studies find that the yearly growth rate of a certain wildflower can be modeled by the equation Y=1000(1.08)^x. Use the properties of exponents to show an equivalent equation that represents the monthly growth of the wildflowers. Find the values of a, b, c, and d. Round to the nearest thousandth as needed.