Answer:
d = 35(4) + 55(t)
Step-by-step explanation:
35 * 4 then added to 55 * the hours that "t" equals will then equal the total distance traveled, d
The distance traveled by a motorist travelling at 35 miles/hour for 4 hours and then at 55 miles/hour for t hours can be expressed as a function of time t, d(t) = 140 + 55t.
Explanation:The subject of this question is functions, which is a topic in Mathematics. To express the total distance traveled as a function of t, we need to use the formula distance = speed x time. The motorist travels at 35 miles per hour for 4 hours, and then at 55 miles per hour for t hours. Therefore, the total distance d can be calculated as follows:
d = (35 mi/h x 4 h) + (55 mi/h x t h).
So, d = 140 mi + 55t mi.
Thus, the total distance traversed by the motorist, expressed as a function of time t in hours, is d(t) = 140 + 55t.
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A line contains the point 0,2. If the slope of the line is m=-6 write the equation of the line using slope intercept form
Answer:
y = -6x + 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-interept (0, b)
We have the slope m = -6 and the point (0, 2) → b = 2.
Substitute:
y = -6x + 2
what is the value of n in the simplified expression?
(4k^7)^3 = 4^n • (k^7)^3 = 64k^21?
Answer:
n = 3Step-by-step explanation:
[tex](4k^7)^3\ \text{it's equal to}\ 64k^{21}\\\\(4k^7)^3\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=4^3(k^7)^3=64k^{7\cdot3}=64k^{21}\\\\4^3(k^7)^3=4^n(k^7)^3\Rightarrow n=3[/tex]
The value of n in the simplified expression is 3.
How to simplify an expression?To simplify an expression approach write an equivalent expression that includes no comparable terms. This means that we will rewrite the expression with the fewest phrases feasible.
What is simplify?Simplifying means to make it less complicated, clearer, or easier. maths to reduce (an equation, fraction, and many others) to a less difficult form by means of cancellation of commonplace factors, regrouping of phrases in the identical variable, etc.
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A deli owner keeps track of the to-go orders each day. The results from last Saturday are shown in the given two-way frequency table.
Saturday's To-Go Deli Orders
In Person By Phone Online Total
Pick Up 38 25 31 94
Delivery 35 28 34 97
Total 73 53 65 191
What percent of the to-go orders were delivery orders placed by phone?
A.
14.66%
B.
38.41%
C.
28.87%
D.
52.83%
Answer:
C
Step-by-step explanation:
Total delivery orders is 97
The number of those placed by phone is 28
So you find the percentage of delivery orders placed by phone by doing 28 divided by 97.
.289 approximately so 28.9% ( I rounded on my answer)
Choice C is the right answer
A cone has a height of 2.5 inches and a radius of 5 inches. What is the volume of the cone?
Answer: [tex]65.44\ in^3[/tex]
Step-by-step explanation:
To calculate the volume of a cone you can use this formula:
[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cone.
In this case you know that this cone has a height of 2.5 inches and a radius of 5 inches. Then:
[tex]h=2.5\ in\\r=5\ in[/tex]
Finally, you need to substitute these values into the formula. Then you get that the volume of the cone is:
[tex]V_{(cone)}=\frac{1}{3}\pi (5\ in)^2(2.5\ in)\\\\V_{(cone)}=65.44\ in^3[/tex]
Find the sample Standard deviation and the population standard deviation of the data set? 17,37,56,16,12,16,19,45,14,37,21,26,43,46,42
Answer:
The sample standard deviation is 14.458
The population standard deviation is 13.967
Step-by-step explanation:
* Lets revise the population standard deviation (σ)
1. Work out the Mean (μ) (average of the numbers)
2. Then for each number subtract the Mean and square
the result (xi - μ)²
3. Then work out the mean of those squared differences
[∑(xi - μ)²/N]
4. Take the square root of that (√[∑(xi - μ)²/N]) and to find σ
* Lets revise the sample standard deviation (s)
1. Work out the Mean (x) (average of the numbers)
2. Then for each number subtract the Mean and square
the result (xi - x)²
3. Then work out the mean of those squared differences [∑(xi - x)²/N - 1]
4. Take the square root of that (√[∑(xi - x)²/N - 1]) and to find s
* Now lets solve the problem
- The data are 15 numbers
17 , 37 , 56 , 16 , 12 , 16 , 19 , 45 , 14 , 37 , 21 , 26 , 43 , 46 , 42
∵ x = μ = sum/number
∴ x = μ = (17+37+56+16+12+16+19+45+14+37+21+26+43+46+42)÷15=29.8
- Subtract the mean from each number and square the result
∵ (17 - 29.8)² = 163.84
∵ (37 - 29.8)² = 51.84
∵ (56 - 29.8)² = 686.44
∵ (16 - 29.8)² = 190.44
∵ (12 - 29.8)² = 316.84
∵ (16 - 29.8)² = 190.44
∵ (19 - 29.8)² = 116.64
∵ (45 - 29.8)² = 231.04
∵ (14 - 29.8)² = 249.64
∵ (37 - 29.8)² = 51.84
∵ (21 - 29.8)² = 77.44
∵ (26 - 29.8)² = 14.44
∵ (43 - 29.8)² = 174.24
∵ (46 - 29.8)² = 262.44
∵ (42 - 29.8)² = 148.84
∴ ∑(xi - μ)² = ∑(xi - x)² = 2926.36
∵ N = 15
∴ The sample standard deviation = √[∑(xi - x)²/(N - 1)]
∴ s = √[2926.36/(15 - 1)] = 14.458
∴ The population standard deviation = √[∑(xi - μ)²/N]
∴ σ = √[2926.36/15] = 13.967
Answer:
B
Step-by-step explanation:
If anyone could please help me with this question???I know that you can get three triangles out of the shape.
Answer:
See below.
Step-by-step explanation:
The triangles are similar because the angles marked 125 are equal and the sides either side of these angle are in the same ratio:
1.3 / 2.5 = 2.6 /5.
If we are given the length of AE we would find CF from the equation:
1.3 / 2.5 = CF / AE
CF = (1.3 * AE) / 2.5.
What is the product?
(-2x- 9y2 )(-4x-3)
Answer:
[tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]
Step-by-step explanation:
Use the FOIL method of multiplying binomials.
First term in each binomial: [tex]-2x * -4x = 8x^2[/tex]
Outside terms: [tex]-2x * -3 = 6x[/tex]
Inside terms: [tex]-9y^2 * -4x = 36xy^2[/tex]
Last term in each binomial: [tex]-9y^2 * -3 = 27y^2[/tex]
Now, rearrange the terms correctly. [tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]
This is our final answer, since it can not be simplified any more.
Answer:
C
Step-by-step explanation:
Edge 2020
consider the explicit formulas for two sequence
These are the formulas right?.. I hope so, anyways..
- f(n)= 2^(n-1) -1
- g(n)=3n+6
f(7)=2^{7-1}-1 - f(7)=2^{6}-1 - f(7)=64-1 - f(7) = 63
g(10)=3\X 10+6 - g(10)=30+6 - g(10) = 36
= f(7)>g(10)
I hope that it helped..
Answer:
The one above is right.
Step-by-step explanation:
What is the measure of arc QR?
26°
52
104
128°
The answer to this question is option C. 104 °
(Late answer!)
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
Over the set of integers, factor the expression x^4– 4x^2 – 12.
Step-by-step explanation:
problem answer in picture
The value of the expression after factorization is (x² + 2)(x² - 6)
What is Factorization?'In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.'
According to the given problem,
[tex]x^{4} - 4x^{2} - 12\\[/tex]
⇒ [tex]x^{4} + 2x^{2} - 6x^{2} - 12\\[/tex]
⇒ [tex]x^{2} (x^{2} +2) -6(x^{2} +2)[/tex]
⇒ [tex](x^{2} +2)(x^{2} -6)[/tex]
Hence, we can conclude the value of the given expression after factorization is [tex](x^{2} +2)(x^{2} -6)[/tex].
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A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist? A. 30 B. 240 C. 2,400 D. 3,000
Answer: Option C
2,400
Step-by-step explanation:
When launching the first 6-sided die there are 6 possible outcomes
When launching the 4-sided die there are 4 possible outcomes
When throwing each die of 10 faces there are 10 possible outcomes
So if all the dice are thrown together, the number of possible combinations that can be obtained is:
[tex]S = 6 * 4 * 10 * 10\\S = 24 * 100[/tex]
[tex]S = 2400[/tex] possible results
Finally the answer is the option C.
The radius of a circular park is 120 m to the nearest meter what is the circumference of the park?
Answer:
D. 754 m
Step-by-step explanation:
When calculating the circumference of the circle it ends up as 753.98 but rounded it's 754.
Answer: It’s 754!
Explanation: I also got this one on a test lol
Solve the equation for X.
(x - 4) - (x + 7) = 8x please help me solve this somebody I don't understand how
Answer:
x = - [tex]\frac{11}{8}[/tex]
Step-by-step explanation:
Given
(x - 4) - (x + 7 ) = 8x
Distribute parenthesis noting second is distributed by - 1
x - 4 - x - 7 = 8x ← simplify left side
- 11 = 8x ( divide both sides by 8 )
x = - [tex]\frac{11}{8}[/tex]
determine the slope and vertical intercept of the following linear function below
X/-4,-2,0,2,4
Y/-114,-60,-6,48,102
what is the slope & what is the vertical intercept ( as an ordered pair ) ?
to get the slope of it, we simply need two points off the table, say (-4,-114) and (2,48). Recall that the y-intercept, where the graph intercepts the y-axis, when that happens x = 0, so is right there on the table already.
[tex]\bf \begin{array}{rrll} x&y\\ \cline{1-2} -4&-114\\ -2&-60\\ 0&-6&\leftarrow y-intercept\\ 2&48\\ 4&102 \end{array}~\hfill (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-114})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{48})[/tex]
[tex]\bf slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{48-(-114)}{2-(-4)}\implies \cfrac{48+114}{2+4}\implies \cfrac{162}{6}\implies 27 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(\stackrel{slope}{27}~~,~~\stackrel{y-intercept}{-6} \right)~\hfill[/tex]
What is 60%off of 35.00$
Hello There!
Amount Saved = Original Price x Discount % / 100. So,
Amount Saved = 35 x 60 / 100
Amount Saved = 2100 / 100
Amount Saved = $21 (answer)
35 - 21 = 14
60% Off of $35.00 Is $14.00
What are the x-intercepts of the graph of the function below?
y = x2 + 2x-15
Answer:
-15
Step-by-step explanation:
the y-intercept would be -15
Answer:
x = - 5, x = 3
Step-by-step explanation:
To find the x- intercepts let y = 0, that is
x² + 2x - 15 = 0
Consider the factors of the constant term (- 15) which sum to give the coefficient of the x- term (+ 2)
The factors are + 5 and - 3, since
5 × - 3 = - 15 and 5 - 3 = + 2, hence
(x + 5)(x - 3) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 3 = 0 ⇒ x = 3
x- intercepts at (- 5, 0) and (3, 0)
in a school there are 320 girls and 500 boys write down the ratio of the number of girls to the number of boys
give your ratio in its simplest form
Answer:
16 : 25
Step-by-step explanation:
The ratio of girls : boys = 320 : 500
To simplify divide both parts by 10
320 : 500 = 32 : 50 ← now divide both parts by 2
32 : 50 = 16 : 25 ← in simplest form
Final answer:
To calculate the simplified ratio of the number of girls to the number of boys in the school, we divide the numbers 320 (girls) and 500 (boys) by their greatest common divisor, which is 80, resulting in the simplest form of 4:6.25 or 16:25.
Explanation:
The question is asking us to find the ratio of the number of girls to the number of boys in a school, and then to simplify this ratio to its simplest form. There are 320 girls and 500 boys in the school. To find the ratio, we compare the number of girls to the number of boys, which gives us 320 to 500.
To simplify the ratio, we look for the greatest common divisor (GCD) that both numbers share. Both 320 and 500 are divisible by 10 for certain, and further simplification can be found by dividing by the GCD of 80. So, if we divide both numbers by 80, we get 4 to 6.25, which simplifies further to a ratio of 4:6.25 or 16:25 when both sides are multiplied by 4. Therefore, the simplified ratio of the number of girls to the number of boys is 16:25.
Urgent!!!!!!
Chad Roth took out a $9,100 simple interest loan at 10% for 36 months. After 27 payments, the balance is $2,526.85. He pays off the loan when the next payment is due.
a.) What is the CURRENT month's interest?
b.) What is the final payment?
Answer:
a) Current Interest is $75.8
b) the final payment will be $11,830
Step-by-step explanation:
Principal Amount = $9,100
Interest rate = 10% or 0.1
Time = 36 months = 3 yeras
Balance after 27 payments = $2,526.85
a) What is the CURRENT month's interest?
The formula to find interest is:
Interest = P*r*t
P= Principal
r = Interest rate
t = time in years
Interest = 9100*0.1*3
Total Interest = 2730
As total period is 36 months so, divide total interest by 36
Current Month Interest = 2730/36
Current Month Interest = 75.8
So, current month interest is $75.8
b) What is the final payment?
The formula used will be
A = P(1+r*t)
A = Final amount
r = interest rate
t = time
Putting values:
A = P(1+r*t)
A = 9100*(1+0.1*3)
A = 9100*(1.3)
A = 11,830
So, the final payment will be $11,830
73 m is equal to ____ dm. (Only input whole number answer.)
Numerical Answers please!
Answer:
73 m is equal to 730 dm
Step-by-step explanation:
We Need to convert 73 m into dm
We know that 1 meter is equal to 10 decimeter
We are given 73 m. Multiply it with 10 and we will get value in decimeter
73*10
= 730 decimeter
So, 73 m is equal to 730 dm
Answer:
The correct answer would be 730 dm.
Step-by-step explanation:
M is the abbreviation of Meter and dm is an abbreviation of Decimeter. A meter is a unit of length as prescribed by the international system of units. This unit is used to measure the length. Decimeter is the smaller unit of meter. 10 Decimeter makes one meter, which means 1M equals 10DM. So where there are 73 meters, there would be 73 * 10 Decimeters in it. This is shown as below.
73 m = 73 * 10 = 730 DM
Find the surface area of a sphere with a diameter of 4 units in terms of pi
Answer:
16π
Step-by-step explanation:
The surface area of a sphere is:
A = 4πr²
where r is the radius, or half the diameter.
If the diameter is 4 units, then the radius is 2 units:
A = 4π (2)²
A = 16π
The surface area is 16π square units.
Seven times a number minus the number is -48. Find the number
Answer:
The number is -8
Step-by-step explanation:
Let
x ---> the number
we know that
The algebraic expression is equal to
[tex]7x-x=-48[/tex]
Solve for x
[tex]6x=-48[/tex]
divide by 6 both sides
[tex]x=-48/6=-8[/tex]
-8 y e s -8 is the answer doods
Solve both questions please ❤️❤️
Answer:
1. y=7.2
2. x=18
Step-by-step explanation:
1. Triangles CMN and CBA are similar triangles (by AAA postulate). Similar triangles have proportional corresponding sides, so
[tex]\dfrac{CM}{CB}=\dfrac{CN}{CA}\\ \\\dfrac{12}{12+y}=\dfrac{10}{10+6}\\ \\12\cdot 16=10\cdot (12+y)\\ \\192=120+10y\\ \\10y=72\\ \\y=7.2[/tex]
2. GK is angle G bisector. Use angle bisector's property:
[tex]\dfrac{GH}{GI}=\dfrac{KH}{KI}\\ \\\dfrac{40}{24}=\dfrac{30}{x}\\ \\40x=24\cdot 30\\ \\4x=24\cdot 3\\ \\x=6\cdot 3=18[/tex]
y = – 3
y = x – 0.8
What is the best approximation for the solution to this system of equations?
(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)
Answer:
(–2.2, –3)
Step-by-step explanation:
y = – 3
y = x – 0.8
Substitute the value of y into the second equation
-3 = x-.8
Add .8 to each side
-3 +.8 = x-.8+.8
-2.2 = x
-3 =y
Answer:
The solution for the system of equations is (–2.2, –3)
Step-by-step explanation:
The solution of the system of equations can be expressed with its components in x and y in the form (x,y) where x is the value of x and y is the value of y. The values of x and y can be found solving the system of equations given.
1. Write the system of equations and name each equation:
[tex]y=-3[/tex] (Eq.1)
[tex]y=x-0.8[/tex] (Eq.2)
2. Replacing Eq. 1 in Eq. 2 and solving for x, we have:
[tex]y=x-0.8[/tex]
[tex]-3=x-0.8[/tex]
[tex]-3+0.8=x[/tex]
[tex]-2.2=x[/tex]
3. Express the answer as the solution tho the system of equations:
(x,y)=(-2.2,-3)
Please help me with this GEOMETRY
Answer: Third Option
[tex]V = 200.96\ in^3[/tex]
Step-by-step explanation:
By definition, the volume of a cone is:
[tex]V = \frac{1}{3}\pi r^2h[/tex]
V is the volume of the cone
h is the height of the cone
r is the radius of the cone
In this case we know that:
[tex]r= 4\ in\\h= 1\ ft[/tex]
We know that in 1 ft there are 12 inches
So
[tex]h=12\ in[/tex]
Now substitute the values of h and r in the formula to obtain the volume of the cone
[tex]V = \frac{1}{3}\pi (4)^2(12)[/tex]
[tex]V = 16*4\pi[/tex]
[tex]V = 200.96\ in^3[/tex]
Polygon ABCD is a rectangle. What is its area? Round your answer to the
nearest tenth.
(2, 5)
(-4, 3)
(-3, 0)
(3, 2)
A. 20.0 square units
B. 19.0 square units
C. 25.6 square units
D. 39.7 square units
Answer:
Option A. 20.0 square units
Step-by-step explanation:
Let
[tex]A(2, 5),B(-4, 3),C(-3, 0),D(3, 2)[/tex]
Plot the points
see the attached figure
The area of the rectangle is equal to
[tex]A=AB*AD[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(2, 5),B(-4, 3)[/tex]
substitute in the formula
[tex]AB=\sqrt{(3-5)^{2}+(-4-2)^{2}}[/tex]
[tex]AB=\sqrt{(-2)^{2}+(-6)^{2}}[/tex]
[tex]AB=\sqrt{40}\ units[/tex]
step 2
Find the distance AD
[tex]A(2, 5),D(3, 2)[/tex]
substitute in the formula
[tex]AD=\sqrt{(2-5)^{2}+(3-2)^{2}}[/tex]
[tex]AD=\sqrt{(-3)^{2}+(1)^{2}}[/tex]
[tex]AD=\sqrt{10}\ units[/tex]
step 3
Find the area of rectangle
[tex]A=AB*AD[/tex]
we have
[tex]AB=\sqrt{40}\ units[/tex]
[tex]AD=\sqrt{10}\ units[/tex]
substitute
[tex]A=(\sqrt{40})*(\sqrt{10})[/tex]
[tex]A=20\ units^{2}[/tex]
what is 5 - j = 3 ????
Answer:
j=2
Step-by-step explanation:
First, subtract by 5 from both sides of equation.
5-j-5=3-5
Simplify.
3-5=-2
-j=-2
Divide by -1 from both sides of equation.
-j/-1=-2/-1
Simplify, to find the answer.
-2/-1=2
It change negative to positive.
j=2 is the correct answer.
I hope this helps you, and have a wonderful day!
Answer:
2
/////////////////////////////////////////////////////////////////////////////////
1st step: again, reverse the equation (by flipping the equation around)
2nd step: do the equation ; 5 - 3 = 2
3rd step: (check your answer) ; 3 plus 2 equals 5
therefore, the answer 2 is correct.
Given that (5,-8) is on the graph of f(x), find the
corresponding point for the function
f(x+2).
Enter the correct answer.
Answer:
The corresponding point is (3,-8)
Step-by-step explanation:
we know that
When you add a constant value (k), to the argument of a function, the graph is shifted k units to the left.
so
In this problem
The rule of the transformation is equal to
f(x) ------> f(x+2)
(x,y) ------> (x-2,y)
(5,-8) -----> (5-2,-8)
(5,-8) -----> (3,-8)
Which equation results from adding the equations in this system? x+6y=9 and -x+2y=-15
Answer:
8y=-6 or 4y=-3
Step-by-step explanation:
We are given two equations
[tex]x+6y=9\\and\\-x+2y=-15[/tex]
In order to add the equations, the left hand side of one equation will be added to the left hand side of second equation. similarly, the right hand side of first equation will be added to the right hand side of the equation so,
[tex]x+6y+(-x+2y)=9+(-15)\\Combining\ alike\ terms\\x+6y-x+2y=9-15\\6y+2y=-6\\8y=-6\\Can\ also\ be\ written \ as\\4y=-3[/tex]
Answer:
The resultant equation is 8y = -6
Step-by-step explanation:
To get the system of equation that will results from adding the statement, we will follow the steps below;
x+6y=9 -------------------------------------------------------------------------------(1)
-x+2y=-15-------------------------------------------------------------------------------(2)
Adding equation (1) and equation(2), we will have;
(1-1)x + (6+2)y =(9-15)
x variable will go away
8y =-6
The resultant equation is 8y = -6
At a Kentucky Friend Chicken, a survey showed 2/3 of all people preferred skinless chicken over the regular chicken. If 2,400 people responded to the survey, how many people preferred regular chicken?
Answer:
800 people
Step-by-step explanation:
We are given in the question that 2/3 of 2400 people preferred skinless chicken.
We have to find the number of people who prefer skinless chicken
[tex]So,\\= \frac{2}{3} *2400\\=1600[/tex]
1600 people prefer skinless chicken,
So,
The number of people who prefer regular chicken = 2400-1600
= 800 people
Answer: kentucky friend chicken? XD
Step-by-step explanation: