Answer:
first number = 89second number = 534third number = 189Step-by-step explanation:
Let the first number be x
Given second number is 6 times a first number.
If first number is x then second number is 6*x = 6x
Given third number is 100 more than the first number
If first number is x then third number is x+100 = x+100
Sum of these three numbers in terms of x
is
sum = x+ 6x+x+100 = 8x+100 __________1
Given, that sum of these numbers is 812.
equating 812 with equation 1 we have,
8x+100 = 812
=> 8x = 812- 100
=> 8x = 712
=> x = 712/8 = 89.
Therefore,
first number = x = 89
second number = 6x = 89*6= 534
third number = x+100 = 89+100 = 189
The three numbers in the problem are 89, 534, and 189. We found these by defining the first number as x, creating equations based on the given relationships, and solving for x.
Let's define the first number as x. According to the problem, the second number would be 6x (as it is 6 times the first number), and the third number would be x + 100 (as it is 100 more than the first number). The sum of these three numbers is given as 812. So, we can set up the equation:
x + 6x + (x + 100) = 812
Combine like terms to simplify the equation:
8x + 100 = 812
Subtract 100 from both sides of the equation:
8x = 712
Divide both sides by 8 to find the value of x:
x = 89
Now that we have the value of the first number, we can find the other two numbers:
The second number is 6 times 89, which is 534.
The third number is 89 + 100, which is 189.
Therefore, the three numbers are 89, 534, and 189.
(e) The number of bees spotted in Amelie's garden can also be modeled by the function B(x) = 50√ k + 2x where x is the daily high temperature, in degrees Fahrenheit, and k is a positive constant. When the number of bees spotted is 100, the daily high temperature is increasing at a rate of 2 ◦F per day. According to this model, how quickly is the number of bees changing with respect to time when 100 bees are spotted?
Answer:
[tex]\frac{dB}{dt}=4[/tex]
Step-by-step explanation:
Derivative indicates rate of change of dependent variable with respect to independent variables. It indicates the slope of a line that is tangent to the curve at the specific point.
Given:
Number of bees is modeled by the function [tex]B(x)=50\sqrt{k}+2x[/tex]
The daily high temperature is increasing at a rate of 2 °F per day when the number of bees spotted is 100.
To find:
rate of change of number of bees when 100 bees are spotted
Solution:
[tex]B(x)=50\sqrt{k}+2x[/tex]
Differentiate with respect to t,
[tex]\frac{dB}{dt}=0+2(\frac{dx}{dt}) \\\frac{dB}{dt}=2(\frac{dx}{dt}) \\[/tex]
Put [tex](\frac{dx}{dt}) =2[/tex]
[tex]\frac{dB}{dt}=2(2)=4[/tex]
At x = 100, [tex]\frac{dB}{dt}=4[/tex]
5g - 10 = -25
please help!
Answer:
g = -3
Step-by-step explanation:
5g - 10 = -25
5g = -25 + 10
5g = -15
g = -15/5
g = -3
hope it helps!
Answer:
g = - 3
Step-by-step explanation:
5g - 10 = - 25
5g = - 25 + 10
5g = - 15
g = - 15 : 5
g = - 3
James and Reggie both collect old coins. Together, they have a total of 60 coins. If James would agree to give 1/4 of his coins to Reggie, they would then have exactly the same number of coins. How many more cons does James have (compared to the number of coins Reggie has)?
Answer:
James has 20 more coins than Reggie
Step-by-step explanation:
Given:
Total number of coins with James and Reggie = 60
If James would agree to give 1/4 of his coins to Reggie, they would then have exactly the same number of coins
To find: number of coins with James and Reggie
Solution:
Let x denote number of coins with James and y denote number of coins with Reggie.
According to question,
[tex]x+y=60\\x-\frac{x}{4} =y+\frac{x}{4} \\x-y=\frac{2x}{4} \\x=2y[/tex]
Put [tex]x=2y[/tex] in [tex]x+y=60[/tex]
[tex]2y+y=60\\3y=60\\y=\frac{60}{3}=20\\ x=2y=2(20)=40[/tex]
So,
number of coins with James = 40
number of coins with Reggie = 20
James has 20 more coins than Reggie
Elena bought a backpacking tent to take with her on hiking trips.
She needs to buy a rain proof tarp for the tent that will cover all 4 sides, as well as protect the ground underneath. Which size tarp should she purchase? *
1 point
a) X-Small: 16 ft²
b) Small: 34 ft²
c) Medium: 88 ft²
d) Large: 104 ft²
e) X-Large: 144 ft²
If the tarp that she buys does not work and the tent fills up completely with water, how much water would it take to fill the tent, if the tent is 8.75 ft tall? *
1 point
a) 140 ft³
b) 144 ft³
c) 48 ft³
d) 46.7 ft³
e) 36 ft³
Answer:
Question 1 = c) Medium: 88 ft²
Question 2 = d) 46.7 ft³
Step-by-step explanation:
Question 1
We would be solving this question by finding the surface area of the tent. The shape of the tent is a square based pyramid.
The surface area of a square based pyramid(tent) =
a² + 2ah
Where in the diagram,
a = base length = 4 ft
h = height of the pyramid (tent ) = 9ft
Surface area = 4² + 2 × 4 × 9
= 16 + 72
= 88ft²
Therefore, the size tarp should she purchase is Medium: 88 ft²
Question 2
For question 2, from the attached diagram, we can see that the diagram is a square based pyramid.
To calculate the amount of water that would fill the square based pyramid, we would have to find the Volume of the tent(square based pyramid).
The formula for the Volume of the tent(square based pyramid) = 1/3(a²h)
Where a = base edge
h = height of the pyramid.
From the diagram,
a = base edge => 4ft.
From the question,
h = height of the tent is given as how tall the tent is = 8.75ft.
Therefore, 1/3(a²h)
1/3 × (4ft)²× 8.75ft
= 46.67ft³
Approximately = 46.7ft³
Therefore, the amount of water it would it take to fill the tent, if the tent is 8.75 ft tall is 46.7ft³
The Vega family must pay $1776 each year in property taxes for their home they pay the tax and equal monthly payments your house payment is $948 a month before the text what is your house payment each month with the tax
Answer:
$1,096.00 per month
Step-by-step explanation:
Divide 1776 by 12 for one payment per month equals 148.
Add the monthly house payment $948 to the monthly tax payment $148. The total monthly payment due is $1,096.00.
The equation y minus two-thirds = negative 2 (x minus one-fourth) is written in point-slope form. What is the equation in slope-intercept form? Y = negative 2 x minus StartFraction 1 Over 6 EndFraction y = negative 2 x + StartFraction 7 Over 6 EndFraction y = negative 2 x + StartFraction 5 Over 12 EndFraction y = negative 2 x minus StartFraction 11 Over 12 EndFraction
Answer:
(B) [tex]y=-2x+ \dfrac{7}{6}[/tex]
Step-by-step explanation:
Given the point-slope form of the equation of a line below:
[tex]y-\dfrac{2}{3}=-2\left(x- \dfrac{1}{4}\right)[/tex]
We are required to write it in the slope-intercept form, y=mx+c.
[tex]y-\dfrac{2}{3}=-2\left(x- \dfrac{1}{4}\right)\\\\y-\dfrac{2}{3}=-2x+ \dfrac{2}{4}\\\\y=-2x+ \dfrac{2}{4}+\dfrac{2}{3}\\\\y=-2x+ \dfrac{7}{6}[/tex]
The slope intercept form is:
[tex]y=-2x+ \dfrac{7}{6}[/tex]
The correct option is B.
Answer:
b
Step-by-step explanation:
An internet company Randomly selected 50 of his customers and ask them how many hours per week to use the Internet of those surveyed 28 use the Internet more than 15 hours per week based on the data if the company has 800 subscribers how many use more than 15 hours per week
Answer:
448 subscribers use more than 15 hours per week
Step-by-step explanation:
In this question, we shall be using the proportion of what was gotten from a survey to estimate the number of subscribers that use more than 15 hours per week
From the question, we can see that out of the 50 people surveyed, 28 use more than 15-hours per week based on data
The proportion that thus use 15-hours per week based on data is 28/50
Now to know the number of subscribers out of 800 that use more than 15-hours per week based on data we have ; 28/50 * 800 = 28 * 16 = 448 subscribers
ahhhhhhhhhh to lazy :(
Answer:
28
Step-by-step explanation:
10 - 12^2 ÷(-2)^3
PEMDAS
Exponents first
10-144÷(-8)
Then multiplication and division
10- (-18)
Then add and subtract
10+18
28
Answer:
why don't you answer mine
Randall buys 3 tickets for a concert for 14.50 each. He gives the cashier a $50 bill. How much change does he get?
Suppose you have the same box with a volume of 400 in^3. And a height of 5 in. You now also know that the box is 8 in. Wide. What is the length of the box?
Answer:
Step-by-step explanation:
Volume of the box = 400 cubic inches
length * width * height = 400
length * 8 * 5 = 400
length * 40 = 400
length = 400/40
length = 10 inches
Answer:
Step-by-step explanatio
it is C
Find the Mean Absolute Deviation: 5,
11, 2, 7, 16. The Mean is 8.2
4.2
3.2.
2.8
1.2
Answer:
4.24
Step-by-step explanation:
It is hard to explain sorry if you need it
The mean absolute deviation of the given values is 4.24
Given the values :
5, 11, 2, 7, 16
Mean = 8.2
The mean absolute deviation = Σ|x - mean| ÷ n
n = number of observations
x = observations
Mean absolute deviation :
(|5 - 8.2| + |11 - 8.2| + |2 - 8.2| + |7 - 8.2| + |16 - 8.2|) ÷ 521.2 ÷ 5 = 4.24Therefore, the mean absolute deviation of the values given is 4.24
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A car is traveling at 65 miles per hour. What happens to the number of miles when the number of hours changes?
VX
O When the number of hours increases, the number of miles decreases.
O When the number of hours increases, the number of miles increases.
O When the number of hours decreases, the number of miles increases
O When the number of hours decreases, the number of miles stays the same.
Mark this and return
Save and Exit
Next
Submit
Answer: The answer is the second one Letter B.
when the number of hours increases, the number of miles increases
Hope this help You Yo.
Find the circumference of a circle with radius, r = 19.5m.
Give your answer in terms of pie
Answer:
39π cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( r is the radius )
Here r = 19.5, thus
C = 2π × 19.5 = 39π cm
need help
What is the volume of this rectangular prism?
What is the volume of this rectangular prism?
A rectangular prism with a length of 6 and one-fourth foot, width of 14 feet, and height of 3 feet.
A:87 and one-half feet cubed
B:131 and one-fourth feet cubed
C:252 feet cubed
D:262 and one-half feet cubed
Answer:
252 feet cubed
hope this helps!
Step-by-step explanation:
Rearrange the equation so xxx is the independent variable.
y+6=5(x-4)y+6=5(x−4)y, plus, 6, equals, 5, left parenthesis, x, minus, 4, right parenthesis
y=
The equation is rearranged so that \(y\) is expressed in terms of[tex]\(x\): y= 5x - 26[/tex]
To rearrange the given equation so that x is the independent variable, you need to solve for y. Here's how you can do it step by step:
1. Start with the given equation:
[tex]\[y + 6 = 5(x - 4)\][/tex]
2. Expand the right side of the equation:
[tex]\[y + 6 = 5x - 20\][/tex]
3. Move the constant term (6) to the right side by subtracting 6 from both sides:
[tex]\[y = 5x - 20 - 6\]\\y = 5x - 26\][/tex]
Now, the equation is rearranged so that \(y\) is expressed in terms of[tex]\(x\): y= 5x - 26[/tex]
For such more question on equation
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The product of 12 and k is 84. Solve for k
Answer:
k=7
Step-by-step explanation
This is the same as 12 x k = 84. To solve, put it into a division problem which is 84 divided by 12. 84 divided by 12 is 7.
A box is filled with 9 red crayons, 5 blue crayons, and 8 yellow crayons. A crayon is chosen at random from the box. Find the probability that it is a blue or a yellow crayon.
Answer:
13/22
Step-by-step explanation:
The total number of crayons in the box
9 red crayons, 5 blue crayons, and 8 yellow crayons = 22
The number that are blue or yellow = 5+8 = 13
P (blue or yellow) = number that are blue or yellow / total
= 13/22
Answer:
13/22
Step-by-step explanation:
Total: 9 + 5 + 8 = 22
Blue or yellow: 5 + 8 = 13
P(Blue or yellow) = 13/22
Which expressions are equivalent to -56z + 28.
A. 1/2 *(-28z + 14
B. (-1.4z+0.7) *40
C. (14 -7z) *(-4)
D.(8z - 4) (-7)
E. -2(-28z-14)
There are 2 right answers. Plz help!
The expressions that are equivalent to -56z + 28 are B. (-1.4z+0.7) * 40 and D.(8z - 4) * (-7), as they both simplify the given expression.
You are looking to find expressions that are equivalent to -56z + 28. Let's simplify each of the given options:
A. 1/2 *(-28z + 14) simplifies to -14z + 7, so this is not equivalent to -56z + 28.
B. (-1.4z+0.7) * 40 simplifies to -56z + 28, which is equivalent.
C. (14 -7z) *(-4) simplifies to -56z + 56, which is not equivalent to -56z + 28.
D.(8z - 4) * (-7) simplifies to -56z + 28, which is equivalent.
E. -2(-28z-14) simplifies to 56z + 28, which is not equivalent since the terms have opposite signs.
The equivalent expressions to -56z + 28 are options B and D.
How many 1/3 cm cubes can fit in a rectangular prism with a length of 5 1/3 cm, a width of 2/3 cm and a height of 1 1/3 cm. PLEASE REPLY QUICKLY I HAVE TO SUBMIT THIS IN 30 MINUTES
Answer:
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
Step-by-step explanation:
D 0,1 of x is?
A. (4,0)
B. (4,1)
C. (5,1)
*20 points!!!*
Answer:
4,0
Step-by-step explanation:
Answer:
i can confirm it is 4,0
Step-by-step explanation:
The Thompson family borrowed $120,000
to buy a house. Over thirty years, they had
to repay 230% of what they borrowed. Find
the total cost of the house.
Answer:
27,600
Step-by-step explanation:
Anika buys a pair of shin guards for $8.58 and several pairs of soccer socks for $4.29 per pair. If she spends $25.74 before taxes, how many pairs of socks does Anika buy?
Answer:
4
Step-by-step explanation:
easier answer
can someone plzzzzzzz help me
A spinner and two cards are shown below.
Which table correctly identifies the sample space of spinning the spinner and then selecting a card? (5 points)
Group of answer choices
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Purple Yellow, Green Red, Green
Green Green, Green Yellow, Yellow Red, Red
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Green Yellow, Yellow Red, Red
Green Green, Purple Yellow, Green Red, Green
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Purple Yellow, Purple Red, Purple
Green Green, Green Yellow, Yellow Red, Red
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Purple Yellow, Purple Red, Purple
Green Orange, Green Yellow, Green Red, Green
Answer:
it the last one
Step-by-step explanation:
only the last option has all the possible combinations
Answer:
Sample space:
{Yellow Purple,
Yellow Green,
Orange Purple
Orange Green,
Red Purple,
Red Green}
What is the mode of the following numbers?
1
,
2
,
4
,
6
,
4
Answer:
4 because mode is always the number that occurs the most. If there were two sixes and two fours, then there would be two modes.
Answer:
4
Step-by-step explanation:
The mode of the data set (a set of distinct values, at least) is the value which appears the most often. In this set, that number is 4.
In a new lottery game, contestants pick 5 numbers (1-9 inclusive) and must guess exactly 3 correct in order to win. What’s the probability of winning this lottery?
Answer: 0.6%
Step-by-step explanation:
We have a selection of 5 numbers, in those selection we have 3 combinations of 3 consecuitve numbers (because the numbers must be in correct order).
The first 3
The 3 in the middle
the last 3.
So a contestant has 3 combinations were he wins.
Now, the number of possible combinations of the 9 numbers given is:
For the first number we have 9 options.
For the second number we have 8 options (because we already selected one)
For the last number we have 7 options (because we already selected 2 numbers)
Then the number of possible combinations is
10*9*8 = 504
The probabilty of winning will be equal to the number of combinations that the contestant has (3) divided by the total number of combinations, this is:
p = 3/504 = 0.006 or 0.006*100% = 0.6%
This pizza has a radius of 4 inches . Which measurement is closest to the area of this pizza in inches?
Answer:
The area is 50.24
Step-by-step explanation:
Area of a circle is
A = πr²
A = 3.14 x 4²
A = 3.14 x 16
A = 50.24
Alex saved $65. He has already spent $25. He plans to spend $8 on a movie ticket each month. Which any quality represents the number of movie tickets he can but?
Answer: 8m+25 ≤ 65
Step-by-step explanation:
Hi, to answer this question we have to write an inequality with the information given:
The product of the number of movie tickets he will buy per month (m) and the price of each ticket (8) plus the already spent money (25) must be less or equal to his savings (65).
Mathematically speaking:
8m+25 ≤ 65
Feel free to ask for more if needed or if you did not understand something.
what is the factorization of x2 + 2x − 63
Answer:
(x+9) (x-7)
Step-by-step explanation:
x^2 + 2x − 63
What 2 numbers multiply to -63 and add to 2
9* -7 = -63
9+-7 = 2
(x+9) (x-7)
Please help me now plz
I will mark you brainliest
Answer:
theta = 24.4 degrees
Step-by-step explanation:
This is a right triangle.
sin theta = opp/ hyp
sin theta = 33/80
Take the inverse of each side
sin^-1 sin(theta) = sin^-1 (33/80)
theta =24.36197794
To the nearest tenth
theta = 24.4 degrees
miguel drove 355 miles using 17 gallons. at this rate , how many gallons of gas would he need to drive 284 miles
Answer:
14.2
Step-by-step explanation:
Answer:
It should be somewhere around 13.6
Step-by-step explanation: