Answer:
number = 25
Step-by-step explanation:
❖ First, let's set up the equation.
"75 less than four times a number" means 4x - 75"is equal to the number" means = n (n = number)n = 4n - 75Solving
Step 1: Subtract 4n from both sides
[tex]n-4n=4n-75-4n[/tex] [tex]-3n=-75[/tex]Step 2: Divide both sides by -3.
[tex]-3n/-3=-75/-3[/tex] [tex]n = 25[/tex]Step 3: Check if solution is correct.
[tex]25=4(25)-75[/tex] [tex]25=100-75[/tex] [tex]25=25[/tex]Therefore, the number is 25.
find the solution set of x² - 7x = -12?
a. {-2, 4}
b. {-4, 1}
c. {4, -4}
d. {3,4}
Answer:
The answer is d.
Step-by-step explanation:
[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\x-3=0; x=3\\x-4=0; x=4\\(3,4)[/tex]
Help me pleasse i need help asap whoever answers it first get brainliest
What is the surface area of this figure?
Enter your answer in the box.
ft²
Complex solid composed of a triangular prism and a rectangular prism. The triangular prism is centered on the top of the rectangular prism. The rectangular prism bottom face is labeled 19 ft and 9 ft. The height of the rectangular prism is labeled 11 ft. The triangular base has an altitude drawn and labeled 12 ft. The sides of the triangle are labeled 13 ft, 13 ft, and 10 ft. The height of the rectangular prism is 9 ft.
The surface area of this figure will be 991 square feet.
What is Surface Area?The area of a plane region or plane field refers to the area of a shape or planar substance, whereas surface area refers to the area of an open surface or the boundary of a multi-object.
A complex solid made out of triangular and rectangular prisms. The triangular prism is centred on the top of the rectangular prism.
The surface area of the shape is given as,
SA = 2(19 x 11 + 11 x 9) + 19 x 9 + 10x 9 + 13 x 12 + 13 x 12
SA= 2(209) + 171 + 90 + 156 + 156
SA = 418 + 171 + 90 + 312
SA = 991 ft²
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Let f(x)=[tex]\footnotesize \rm \lim_{n \to \infty } \left \lgroup \frac{ {n}^n(x + n) \bigg( x + \dfrac{n}{ 2} \bigg) \dots \bigg(x + \dfrac{n}{n} \bigg)}{n!( {x}^{2} + {n}^{2}) \bigg( {x}^{2} + \dfrac{ {n}^2 }{4} \bigg) \dots \bigg( {x}^{2} + \dfrac{ {n}^{2} }{ {n}^{2} } \bigg) } \right \rgroup^{ \dfrac{x}{n} } \\ [/tex] , for all x > 0. Then
[tex]\rm(A) \: f \bigg( \dfrac{1}{2} \bigg ) \geq f(1)[/tex]
[tex]\rm(B) \: f \bigg ( \dfrac{1}{3} \bigg) \leq f \bigg ( \dfrac{2}{3} \bigg)[/tex]
[tex]\rm(C) \: f'(2) \leq0[/tex]
[tex] \rm(D) \: \frac{f'(3)}{f(3)} \geq \frac{f'(2)}{f(2)} \\ [/tex]
Use the old exp-log trick and properties of the logarithm to rewrite the limit as
[tex]\displaystyle \lim_{n\to\infty} \left(\frac{n^n \left(x+\frac n1\right) \left(x+\frac n2\right) \cdots \left(x+\frac nn\right)}{n! \left(x^2+\left(\frac n1\right)^2\right) \left(x^2+\left(\frac n2\right)^2\right) \cdots \left(x^2+\left(\frac nn\right)^2\right)}\right)^{\frac xn}[/tex]
[tex]\displaystyle = \exp\left[\lim_{n\to\infty} \frac xn \ln \left(\frac{n^n \left(x+\frac n1\right) \left(x+\frac n2\right) \cdots \left(x+\frac nn\right)}{n! \left(x^2+\left(\frac n1\right)^2\right) \left(x^2+\left(\frac n2\right)^2\right) \cdots \left(x^2+\left(\frac nn\right)^2\right)}\right)\right][/tex]
[tex]\displaystyle = \exp\left[x \lim_{n\to\infty}\frac1n\ln\left(\frac{n^n}{n!}\right) + \frac1n \sum_{k=1}^n \ln\left(x+\frac nk\right) - \frac1n \sum_{k=1}^n \ln\left(x^2+\left(\frac nk\right)^2\right)\right][/tex]
[tex]\displaystyle = \exp\left[x \lim_{n\to\infty}\frac1n\ln\left(\frac{n^n}{n!}\right) + \frac1n \sum_{k=1}^n \ln\left(x+\frac1{k/n}\right) - \frac1n \sum_{k=1}^n \ln\left(x^2+\frac1{\left(k/n\right)^2}\right)\right][/tex]
The first limit converges to 0, since n! asymptotically behaves like nⁿ, so ln(nⁿ/n!) → ln(1) = 0.
The two remaining sums converge to definite integrals:
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \ln\left(x + \frac1{\frac kn}\right) = \int_0^1 \ln\left(x + \frac1y\right) \, dy = \frac{(x+1) \ln(x+1)}x[/tex]
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \ln\left(x^2 + \left(\frac1{\frac kn}\right)^2\right) = \int_0^1 \ln\left(x^2 + \frac1{y^2}\right) \, dy = \frac{2\tan^{-1}(\sqrt x)}{\sqrt x} + \ln(1+x)[/tex]
It follows that
[tex]f(x) = \exp\left[x\left(0 + \dfrac{(x+1)\ln(x+1)}x - \dfrac{2\tan^{-1}(\sqrt x)}{\sqrt x} - \ln(x+1)\right)\right][/tex]
[tex]f(x) = \exp\left[\ln(x+1) - 2\sqrt x \tan^{-1}(\sqrt x)\right][/tex]
[tex]f(x) = (x+1) e^{-2\sqrt x \tan^{-1}(\sqrt x)}[/tex]
By computing f'(x) and f''(x), it's easy to show that f'(x) ≤ 0 and f''(x) ≥ 0 for all x > 0. So f(x) is decreasing and f'(x) is increasing, and
• (A) f(1/2) ≥ f(1) is true
• (B) f(1/3) ≤ f(2/3) is false
• (C) f'(2) ≤ 0 is true
• (D) f'(3)/f(3) ≥ f'(2)/f(2) ⟺ f'(3)/f'(2) ≥ f(3)/f(2) ⟺ (something larger than 1) ≥ (something smaller than 1) is true
what are the partial products when finding 1,643×4.
Answer:
4,000
600
160
12
Step-by-step explanation:
When using partial products, you basically break up the number into ones, tens, hundreds, thousands, etc.
So the partial products of 1,643 x 4 will be,
1,000 x 4
600 x 4
40 x 4
3 x 4
The partial products of the multiplication problems are,
4000
600
160
12
The answer will be 4,772.
The partial products of the multiplication problems are,
4000, 2400, 160 and 12
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
When using partial products, you basically break the number into ones, tens, hundreds, thousands, etc.
So the partial products of 1,643 x 4 will be,
1,643 can be written as 1000+600×40+3.
Now multiply with 4.
(1000+600×40+3)×4
1,000 x 4+600 x 4+40 x 4+3 x 4
4000+2400+160+12
Hence the partial products of the multiplication problems are,
4000, 2400, 160 and 12 and The answer will be 4,772.
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93x + 7 = 95x - 3
Solve the equation
Answer:
x=5
Step-by-step explanation:
thanks again everyone
Answer:
4x^3
Step-by-step explanation:
GCF is the Greatest Common Factor
12x^6 + 4x^4 + 28x^3
= 4x^3(3x^3 + x + 7)
GCF is 4x^3
The total yearly cost to rent a trumpet is $114. The monthly cost is constant with no initial fee.
A person rents a trumpet for 3 years and 5 months.
Show your work or explain how you would find the total cost, in dollars, for the person to rent the trumpet?
Write an equation that represents the relationship between m, the number of months a trumpet is rented, and t, the total cost to rent the trumpet.
Explain your equation.
Enter your answer and your work or explanation in the space provided.
Step-by-step explanation:
There are 12 months in a year so,
114/12= 9.5$/month
t=9.5m
Since T represents the total cost, we want to express it in terms of months by multiplying m which refers to the number of months by the monthly fee which i have already calculated.
Using this equation we can find out the answer to your previous question.
t=9.5m
but m=3×12+5=41 months (3 years 12 months each)
t=9.5(41)
t=389.5 $
In Martina's bucket there are 6 brown worms and 7 red worms.
Martina is going to choose 9 worms at random from the bucket to use for fishing.
What is the probability that she will choose 4 brown worms and 5 red worms? Round your answer to three decimal places.
Which of the binomials below is a factor of this trinomial?
x^2 - 13x + 30
A. x + 5
B. x - 10
C. x^2 + 5
D. x + 6
Answer:
B. x - 10
Step-by-step explanation:
x² - 13x + 30 = (x - 3)(x - 10)
x² + (a + b)x + ab = (x + a)(x + b)
PLEASE HELPPP!:( i’ll mark brainlest!
What is the sum of all positive 1 digit integers that 4221462 is divisible by?
9514 1404 393
Answer:
19
Step-by-step explanation:
The prime factorization of 4221462 is ...
4221462 = 2·3·7·100511
so, the 1-digit divisors are ...
1, 2, 3, 6, 7
The total of these numbers is 19.
Sergio found 4 pennies on the ground his sister said that she found 2times as many pennies Sergio figured out that his sister found 6 pennies .what did Sergio do wrong
Answer:
Sergio found 4 pennies on the ground and her sister said that she found twice as many as him
When his sister said that she found twice as many, sergio added 2 to his number of pennies instead of multiplying by 2
That's where Sergio made a mistake and got the answer wrong
if f(a)=b and g(b)=c are functions then domain and range of fog and gof equals to
Answer:
fog =gofthen it will be equal
Which words have vertical symmetry for all of the letters in the word? Check all that apply.
MOM
DIZZY
НІТ
SEAT
WAXY
Answer:
MOM
HIT
WAXY
I just did this on edge
Answer:
1 3 6
Step-by-step explanation:
Write the ratio in the simplest form 25 to 45
Answer: 5/9 is the simplified fraction for 25/45 by using the GCD or HCF method. Thus, 5/9 is the simplified fraction for 25/45 by using the prime factorization method.
if m x and l m = 6 and l = 2 find the value of l when m = 15
Answer:
5
Step-by-step explanation:
6 / 2 = 15 / l
3 = 15 / l
l = 15 / 3
l = 5
How far from the door must a ramp begin in order to rise 5 ft with an 11-degree angle of elevation? Round off your answer to the nearest hundredth.
PS. Please put a drawing/illustration. Thank you!
The door of the ramp must begin at a distance of 25.72ft in order to raise the ramp by 5ft.
Data;
height (opposite) = 5ftangle = 11°distance (adjacent) =xTrigonometric RatioTo solve this problem, this is a right angle triangle and we can use trigonometric ratio SOHCAHTOA here.
Since we have the value of angle and opposite and solving only for adjacent, we can use tangent of the angle.
[tex]tan \theta = \frac{opposite}{adjacent} \\[/tex]
Let's substitute the values into the formula above and solve
[tex]tan 11 = \frac{5}{x} \\x = \frac{5}{tan 11} \\x = 25.72ft[/tex]
The door of the ramp must begin at a distance of 25.72ft in order to raise the ramp by 5ft.
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Question 1 Solve 18>12+x. Graph the solution. The solution is .
Answer:
6 greater than x
Step-by-step explanation:
I did the math on paper
How can I fing the volume of a fish tank?
Answer:
You can measure from the inside of the tank or measure the outside and subtract the width of the tank walls to find the inside measurement. Next multiply the length width and depth measurements to find the cubic volume in cubic inches
Step-by-step explanation:
P = 0.5e - 5 to determine P
Answer:
Let's solve your equation step-by-step.
p=(0.5)(2.718282)−5
Step 1: Simplify both sides of the equation.
p=(0.5)(2.718282)−5
p=1.359141+−5
p=(1.359141+−5)(Combine Like Terms)
p=−3.640859
p=−3.640859
Answer:
p=−3.640859
Step-by-step explanation:
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.
Answer:divide both sides of the equation by 10.4
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
help. I cant seem to figure this out.I'll give brainliiest.
Tom is reading an article about the population of a city. The city's exact population is 175,901 people. Tom says that the city's population rounded to the nearest thousand is 175,000. Is Tom correct?
Answer:
nope, it’s actually 176,000. the 901 is very high if u compare it to 499 which is the lowest number to round down to.
Step-by-step explanation:
A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age are related to annual income. A sample of 20 employees is selected and the data are given below. Education (No. of years) Length of tenure in current employment (No. of years) Age (No. of years) Annual income ($) 17 8 40 124,000 12 12 41 30,000 20 9 44 193,000 14 4 42 88,000 12 1 19 27,000 14 9 28 43,000 12 8 43 96,000 18 10 37 110,000 16 12 36 88,000 11 7 39 36,000 16 14 36 81,000 12 4 22 38,000 16 17 45 140,000 13 7 42 11,000 11 6 18 21,000 20 4 40 151,000 19 7 35 124,000 16 12 38 48,000 12 2 19 26,000 10 6 44 124,000 a. Determine the estimated multiple linear regression equation that can be used to predict the annual income given number of years school completed (Education), length of tenure in current employment, and age.
Answer:
y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3
Step-by-step explanation:
Given the data below:
Education (No. of years) Length of tenure in current employment (No. of years) Age (No. of years) Annual income ($) 17 8 40 124,000 12 12 41 30,000 20 9 44 193,000 14 4 42 88,000 12 1 19 27,000 14 9 28 43,000 12 8 43 96,000 18 10 37 110,000 16 12 36 88,000 11 7 39 36,000 16 14 36 81,000 12 4 22 38,000 16 17 45 140,000 13 7 42 11,000 11 6 18 21,000 20 4 40 151,000 19 7 35 124,000 16 12 38 48,000 12 2 19 26,000 10 6 44 124,000
The estimated multiple linear regression equation that can be used to predict the annual income using number of years school completed (Education), length of tenure in current employment, and age using an online multiple regression calculator is :
y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3
According to the general form of a multiple linear regression model:
-143481.1924 = intercept(c) ; where regression line crosses the origin
10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3
y = predicted variable
Where the regression line crosses the origin 10011.92x₁ – 2193.88x₂ + 2689.24x₃ are weight coefficients of the three predictor variables x₁, x₂, and x₃. Then y is the predicted variable.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more two variables.
A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age are related to annual income.
A sample of 20 employees is selected.
The estimated multiple linear regression equation that can be used to predict the annual income using the number of years of school completed (Education), length of tenure in current employment, and age using an online multiple regression calculator will be
[tex]\rm y=-143481.19 + 10011.92x_1-2193.88x_2+2689.24x_3\\[/tex]
According to the general form of a multiple linear regression model will be
[tex]\rm -143481.19 = intercept (C)[/tex]
Where the regression line crosses the origin 10011.92x₁ – 2193.88x₂ + 2689.24x₃ are weight coefficients of the three predictor variables x₁, x₂, and x₃.
y = predicted variable.
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Complete the table by writing the two missing forms of the number. Make sure your fractions are reduced to lowest terms.
Answer: Look at picture
Answer:
a.) 0,51
b.) 51%
c.) 1/100
d.) 1%
e.) 3/20
f.) 0,15
Step-by-step explanation:
[tex]a.) \: \frac{51}{100} = 51 \div 100 = 0.51[/tex]
[tex]b.) \: \frac{51}{100} = 51\%[/tex]
[tex]c.) \: 0.01 = \frac{1}{100} [/tex]
[tex]d. )\: 0.01 = \frac{1}{100} = 1\%[/tex]
[tex]e.) \: 15\% = \frac{15}{100} = \frac{3}{20} [/tex]
[tex]f.) \: 15\% = \frac{15}{100} = 0.15[/tex]
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Slove for x
Show all work
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
[tex]x^2=8(8+42)[/tex]
[tex]x^2=8*50[/tex]
[tex]x=20[/tex]
~
Which angles are adjacent to each other?
Answer:
Angles 7 and 8
Step-by-step explanation:
They are next to each other, and share a common side.
What is the gradient of the graph shown?
Gradient = Slope.
Use two points on the line to find the slope.
Slope = change in y over change in x
Points: (-4,0) and (0,-4)
Slope = (-4 - 0) / (0 - -4)
Slope = -4/4 = -1
Slope = -1
Lines M and N are parallel. Name the relationship between ∠a and ∠b.
Answer: A
Step-by-step explanation: