Step 1. The information that we have is:
The aquarium is filled to a depth of 4/5 meters in 8 minutes.
Required: Find the unit rate in minutes per meter.
Step 2. First, we convert 4/5 meters to a decimal number:
[tex]\frac{4}{5}\text{ meters }=0.8\text{ meters}[/tex]Step 3. To find the unit rate, we need to divide the number of minutes by the number of meters:
[tex]\frac{8minutes}{0.8\text{ meters}}[/tex]The result is:
[tex]10\text{ minutes per meter}[/tex]The unit rate is 10 minutes per meter.
Answer: 10
I need 5 points. the vertex, 2 to the left, and 2 to the right
Graph the parabola
[tex]\begin{gathered} y=x^2-10x+27 \\ f(x)=ax^2+bx+c \end{gathered}[/tex]In order to find the vertex (h,k), we can use this formula
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=f(h) \end{gathered}[/tex]where,
a = 1
b = -10
c = 27
then, the vertex (h,k) is
[tex]\begin{gathered} h=-\frac{-10}{2\cdot1}=\frac{10}{2}=5 \\ k=f(5)=5^2-10\cdot5+27=25-50+27=2 \end{gathered}[/tex]Therefore, vertex is the point (h,k) = (5,2)
Now, we just need two points to the left and two points to the right of this point
for example, when x = 3, then y = 6
[tex]f(3)=3^2-10\cdot\: 3+27=6[/tex]when x = 4, then y = 3
[tex]f(4)=4^2-10\cdot\: 4+27=3[/tex]when x = 6, then y = 3
[tex]f(6)=6^2-10\cdot\: 6+27=3[/tex]when x = 7, then y = 6
[tex]f(7)=7^2-10\cdot\: 7+27=6[/tex]Thus, the set of 5 points is the following:
[tex](3,6),(4,3),(5,2),(6,3),(7,6)[/tex]What are the known solution to you can see the solution in the picture
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The known solutions to:
[tex]f(x)\text{ = g(x) are:}[/tex][tex]\begin{gathered} \text{when x= 1,} \\ f(1)\text{ = 14,} \\ g(1)\text{ = 14} \\ \text{and } \\ \text{when x = 9 ,} \\ f(1)\text{ = 6} \\ g(1)\text{ = 6} \end{gathered}[/tex]CONCLUSION:
The correct answers are:
[tex]\begin{gathered} \text{ x = 1 -- OPTION A} \\ \text{and } \\ \text{x = 9 }--\text{OPTION D} \end{gathered}[/tex]There are 45 students in the 4th grade at Akili Academy. If Ms. Lause found out that 68% of them attended the football game over the weekend, how many students attended the game? You may have to round to the closest whole student.
There are 45 students in the 4th grade at Akili Academy. If Ms. Lause found out that 68% of them attended the football game over the weekend, how many students attended the game? You may have to round to the closest whole student.
we have that
45 students represents -------> 100%
so
Applying proportion
Find out how much students represents 68%
45/100=x/68
solve for x
x=(45/100)*68
x=30.6
therefore
the answer is 31 studentsDefine the domain of the following:A. -3,-2,-1,0,1,2,3,4,5,6,7,8,B. 3,-1,2,0,-2C. -3,-1,1,3,6D. All real numbers
The domain is the values of x in the given graph
Since the graph is some points
(-3, 3), (-1, -1), (1, 2), (3, 0), (6, -2)
Then the domain is the x-coordinates of all point
D = {-3, -1, 1, 3, 6}
The answer is C
Based on the graph, what are the solutions of theequationx^3 - 6x^2 + 9x = 0?x = 3x= -3,0 x = 0,3 x = -3, 0,3
SOLUTION
The image of the graph is giving below
Based on the graph above, the solutions of the equation is at the point where the curve touches the x-axis
Hence the solution to the equation
[tex]x^3-6x^2+9x=0[/tex]is
[tex]undefined[/tex]Therefore the third option is correct
What is the Effective Annual Yield in percent when the annual nominal interest rate is 7.042% compounded quarterly?EAY = ___%
Answer:
Given that,
Annual nominal interest rate is 7.042% compounded quarterly
To find the effective annual yield.
Explanation:
The formula for calculating effective annual yield (E) is,
[tex]E=(1+\frac{r}{n})^n-1[/tex]where r is the interest rate, n is the number of compounds per year.
Here, r=7.042 % and n=4
Substitute the values we get,
[tex]E=(1+\frac{7.042}{100\times4})^4-1[/tex][tex]E=(1+0.017605)^4-1[/tex][tex]E=1.07230154-1[/tex][tex]E=0.07230154[/tex][tex]E=0.07230154\approx7.23\%[/tex]Effective annual yield is 7.23%
please help! i’ll give points.
Answer:
87
Step-by-step explanation:
112+74=186
360-186=174
174/2=87
Hi, can you help me to solve this exercise, please!!
Given the Right Triangle BCD, you know that:
[tex]\begin{gathered} BD=8 \\ m\angle BCD=63\degree \end{gathered}[/tex]Then, you can use the following Trigonometric Function in order to find the length of the side CD:
[tex]\sin \beta=\frac{opposite}{hypotenuse}[/tex]In this case:
[tex]\begin{gathered} \beta=63\degree \\ opposite=BD=8 \\ hypotenuse=CD \end{gathered}[/tex]Therefore, substituting values and solving for CD, you get:
[tex]\begin{gathered} \sin (63\degree)=\frac{8}{CD} \\ \\ CD\cdot\sin (63\degree)=8 \end{gathered}[/tex][tex]\begin{gathered} CD=\frac{8}{\sin(63\degree)} \\ \\ CD\approx9.0 \end{gathered}[/tex]Hence, the answer is:
[tex]CD=9.0[/tex]PLEASE HELP!!!!! (31 POINTS!) Fill in the arithmetic table
The table for this arithmetic sequence should be completed as follows:
Position 1 6 8 11 19 25
Term 0 -10 -14 -20 -36 -48
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference by using the 25th term of this arithmetic sequence:
-48 = 0 + (25 - 1)d
-48 = 24d
d = -48/2
d = -2.
For the nth term of this arithmetic sequence with -10, we have:
aₙ = a₁ + (n - 1)d
-10 = 0 + (n - 1)-2
-10 = -2n + 2
2n = 12
n = 6.
For the 8th term of this arithmetic sequence, we have:
a₈ = a₁ + (n - 1)d
a₈ = 0 + (8 - 1)-2
a₈ = -14.
For the nth term of this arithmetic sequence with -20, we have:
aₙ = a₁ + (n - 1)d
-20 = 0 + (n - 1)-2
-20 = -2n + 2
2n = 22
n = 11.
For the 19th term of this arithmetic sequence, we have:
a₁₉ = a₁ + (n - 1)d
a₁₉ = 0 + (19 - 1)-2
a₁₉ = -36.
Read more on arithmetic sequence here: brainly.com/question/24989563
#SPJ1
Evaluate the expression, writing the result as a simplified complex number.My answer 3iI know is wrong but I don’t know why.
The first thing we can do is solve the i cubed:
[tex]undefined[/tex]Thomas is buying football jerseys for his high school football team. Thecost of each jersey is $80. The company also charges a processing fee of$100.Write an equation that represents Thomas' total cost for purchasing xnumber of jerseys.What is Thomas' total cost, if he buys 55 jerseys?
Thomas is buying football jerseys for his high school football team.
The cost of each jersey is $80.
The company also charges a processing fee of $100.
We could write an equation that models Thomas's total cost for purchasing x
number of jerseys.
Since for every x jerseys Thomas buys, he pays
[tex]80x\text{ dollars}[/tex]But he also has to pay the company's processing fee, this is independent of the quantity bought.
So, the total cost for buying x number of jerseys is;
[tex]y=80x+100\text{ dollars}[/tex]ii. What is Thomas's total cost, if he buys 55 jerseys?
We can use our formula,
[tex]\begin{gathered} y=80x+100\text{ , when x =55, we have;} \\ y=80(55)+100 \\ y=4400+100 \\ y=4500\text{ dollars} \end{gathered}[/tex]Therefore, Thomas's total cost for 55 jerseys is $4500
20. A fast food restaurant estimates the cost of making hamburgers to be $2.05 per hamburger plus an additional cost of $2,000 for facility expenses. If $13,025 represents the total cost of making x hamburgers, which equation can be used to find the number of hamburgers produced?A. 13,025=2.05+2,000 xB. 13,025=2.05 x+2,000C. 13,025 x=2.05+2,000D. 13,025=2.05+2000 x
Answer:
(B)13,025=2.05x+2,000
Explanation:
The cost of making one hamburger = $2.05
The cost of making two hamburgers = $2.05 x 2
Therefore:
The cost of making x hamburgers = $2.05x
Since there is an additional cost of $2,000 for facility expenses.
The total cost will be:
[tex]2.05x+2000[/tex]If $13,025 represents the total cost of making x hamburgers, then:
[tex]13,025=2.05x+2000[/tex]This is the equation that can be used to find the number of hamburgers produced.
The correct choice is B.
Find the image of (1,2) after a reflection about x=3 followed by a reflection about x=7.
EXPLANATION
Given the point (1,2), if we reflect the point the new image must be at the same distance from the reflective line just at the original image.
Therefore when (1,2) is reflected over x= 3 the image becomes
[tex](5,2)[/tex]As the distance between line x=3 is 2 units on both sides.
When we then reflect (5,2) over x =7, using the same idea above the image becomes
Answer:
[tex](9,2)[/tex]simplify the expression so there is only one positive power for the base -5
When we are dividing, exponents are subtracted!
The rule is shown below:
[tex]a^b\div a^c=a^{b-c}[/tex]We can apply this rule to this problem as shown:
[tex]\begin{gathered} -5^7\div-5^2 \\ =-5^{7-2} \\ =-5^5 \end{gathered}[/tex]Did you turn the volume of the cylinder given. Calculate using pi on calculator and grounded to the nearest tenth. Is the correct option A, B, or C?
V= 14726 ft^3
Given K is the midpoint of line segment CR, line segment MA bisects angle CMR. conclusion?
From the given image, on which you have that MA bisect angle CMR, you can conclude:
- Inside the parallelogram ACMR you have four congruent triangles.
- Angles MKR and CKA are congruent, that is, these angles have the same measure.
- Angles CKM and AKR are congruent.
Please answer correctly! Giving brainliest!
Describe in words where cube root of 30 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
Answer:
A) Between 3 and 4, but closer to 3======================
First, find the cubes of 2, 3 and 4 and then compare them with 30.
2³ = 8,3³ = 27,4³ = 64We see that 30 is between 27 and 64 and is closer to 27:
27 < 30 < 64Therefore cube root of these numbers are:
∛27 < ∛30 < ∛643 < ∛30 < 4So the ∛30 is between 3 and 4 and closer to 3.
Correct answer choice is A.
Answer:
A) Between 3 and 4, but closer to 3.
Step-by-step explanation:
A perfect cube is the result of multiplying the same integer three times.
First few perfect cubes: 1, 8, 27, 64, 125, etc.To estimate the value of the cube root of a number, find the perfect cubes above and below the number:
The perfect cubes either side of 30 are:
27 < 30 < 64Therefore, the cube roots are:
[tex]\implies \sf \sqrt[3]{27} < \sqrt[3]{30} < \sqrt[3]{64}[/tex]
[tex]\implies \sf 3 < \sqrt[3]{30} < 4[/tex]
As 30 is closer to 27 than 64, the cube root of 30 is closer to the cube root of 27 than the cube root of 64.
Therefore, the cube root of 30 would be plotted on a number line:
between 3 and 4, but closer to 3.For Monday morning's staff meeting, Jim bought 3 bags of bagels and 3 packages of cream cheese and paid $16.50 (excluding sales tax).For Friday's meeting, he bought 5 bags of bagels and 2 packages of cream cheese and paid $22.25 (again, excluding sales tax). How much dobags of bagels and packages of cream cheese cost?
Answer:
Explanation:
Let the price of one bag of bagel = b
Let the price of one package of cream cheese = c
3 bags of bagels and 3 packages of cream cheese costs $16.50.
[tex]3b+3c=16.50\cdots(1)[/tex]5 bags of bagels and 2 packages of cream cheese costs $22.25.
[tex]5b+2c=22.25\cdots(2)[/tex]Thus, we derive a system of two linear equations which we then solve for b and c.
[tex]\begin{gathered} 3b+3c=16.50\operatorname{\cdots}(1) \\ 5b+2c=22.25\operatorname{\cdots}(2) \end{gathered}[/tex]Multiply equation 1 by 5 and equation 2 by 3.
[tex]\begin{gathered} 15b+15c=82.5 \\ 15b+6c=66.75 \end{gathered}[/tex]Subtract to eliminate b.
[tex]9c=15.75[/tex]Divide both sides by 9:
[tex]\begin{gathered} \frac{9c}{9}=\frac{15.75}{9} \\ c=1.75 \end{gathered}[/tex]Next, substitute c=1.75 into equation 1.
[tex]\begin{gathered} 3b+3c=16.50 \\ 3b+3(1.75)=16.50 \\ 3b=16.50-3(1.75)=11.25 \\ b=\frac{11.25}{3}=3.75 \end{gathered}[/tex]The price per bag of bagel is $3.75 and the price per package of cream cheese is $1.75.
Write the function below in slope intercepts form. Show all the steps
we need to find the equation in the form y=mx+b, so:
4x+y=5
y=-4x+5
the "4x" go subtracting to the other side
and we have m=-4 and b=5
so the answer is: y=-4x+5
Exercises 11.3- omplete the following: Find the slope of a line parallel to the line through the points. (a) (2, 5) and (4, -6)
If the lines are parallel then the slopes will be equal
The slope is the ratio of the rate of change in y coodinate with respect to rate of change in x coordinate
[tex]\text{ Slope=}\frac{y_2-y_1}{x_2-x_1}_{}[/tex]The given pair of coordinates : (2,5) and (4,-6)
[tex]\begin{gathered} \text{ Slope = }\frac{-6-5}{4-2} \\ \text{ Slope=}\frac{-11}{2} \end{gathered}[/tex]The slope of the line is -11/2
The slope of the line parallel to line whose coordinates are (2,5) and (4,-6) is -11/2
Which of the equations will be a true statement if p = 10 3 ? Select the two choices that apply. A.
3
.
4
÷
p
=
0
.
034
B.
437
÷
p
=
0
.
437
C.
53
.
45
÷
p
=
53
.
45
D.
6
,
340
÷
p
=
6
.
34
E.
2
,
458
.
2
÷
p
=
24
.
582
The linear equation in one variable is used to know on e unknown quantity. The correct answer is option a.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
Given that,
The value of p = 10.3
Substitute p = 10.3 in all the given option as,
(a)
3.4 ÷ p = 0.34
Substitute p = 10.3 in the above equation to get,
LHS = 0.33
Since LHS = RHS
The given option is true.
(b)
437 ÷ p = 0.437
Substitute p = 10.3 in the above equation to get,
LHS = 42.427
Since LHS ≠ RHS
The given option is not true.
(c)
53.45 ÷ p = 53.45
Substitute p = 10.3 in the above equation to get,
LHS = 5.18
Since LHS ≠ RHS
The given option is not true.
(d)
340 ÷ p = 6.34
Substitute p = 10.3 in the above equation to get,
LHS =33
Since LHS ≠ RHS
The given option is not true.
(e)
2458 ÷ p = 24.582
Substitute p = 10.3 in the above equation to get,
LHS =238.64
Since LHS ≠ RHS
The given option is not true
Hence, the value of p satisfies only for option a.
To know more about linear equation click on,
brainly.com/question/11897796
#SPJ1
you rent a moving van you have to pay a flat fee of $99 plus $0.50 per mile you drive 120 miles how much does it cost to drive the van also I NEED work
It cost $159 to drive the van for 120 miles
Explanation:
The flat fee of the van = $99
The charge per mile = $0.50
Let m represent the number of miles
T = total cost
The total cost becomes:
T = 0.5m + 99
When you drive 120 miles, m = 120 miles
T = 0.5(120) + 99
T = 60 + 99
T = $159
Hence, it cost $159 to drive the van for 120 miles
Which option shows a DISCRETE data set? >>> CORRECT ANSWER: The NUMBER OF CARS that I pass through an intersection EVERY HOUR. >> Why is this discrete? Your answer
Discrete measure:
Assumes countable values. For example, 0, 1, 2, 3,...
It does not assume decimal numbers, for example 2.5. There is not half a car, so the number of cars will always be a discrete measure.
Calculate the population variance and population standard deviation for the following data said if necessary round to one more decimal place than the largest decimal
Given the dataset
2, 3, 4, 5, 6, 7, 8, 9, 10, 11
range is given by
[tex]range=maxValue-MinValue[/tex][tex]range=11-2[/tex][tex]range=9[/tex]Range=9
population variance is given by
[tex]s^2=\frac{SumSquares}{n}[/tex][tex]s^2=\frac{82.5}{10}[/tex][tex]s^2=8.25[/tex]rounded
population variance = 8.3
population standar deviation is given by
[tex]std=\sqrt{\frac{SumSquares}{n}}[/tex][tex]std=\sqrt{8.25}[/tex][tex]std=2.872[/tex]rounded
population standar deviation= 2.9
A circular garden with a radius of 4 ft is planted in the center of a 10 ft square. The part of the square that is NOT the garden is covered with small white rocks. what is the area of the region covered with white rocks?
First, draw a diagram to visualize the situation:
The area of the region covered with small rocks can be found by subtracting the area of the circle from the area of the square.
The area A_s of a square with side L is given by:
[tex]A_s=L^2[/tex]And the area A_c of a circle with radius r is given by:
[tex]A_c=\pi r^2[/tex]Replace r=4ft and L=10ft into the equations to find the area of the circle and the square:
[tex]\begin{gathered} A_s=(10ft)^2=100ft^2 \\ A_c=\pi(4ft)^2=16\pi ft^2\approx50.265ft^2 \end{gathered}[/tex]Finally, subtract the area of the circle from the area of the square to find the area of the region covered with rocks:
[tex]A=A_s-A_c=100ft^2-16\pi ft^2\approx49.7ft^2[/tex]Therefore, the area of the region covered with rocks is exactly 100-16π square feet, which is approximately equal to 49.7 square feet.
I have to find the length of x but I need guidance
Since we are dealing with a right triangle, we can use trigonometric identity below
[tex]\begin{gathered} sin\theta=\frac{O}{H} \\ \theta\rightarrow\text{ interior angle} \\ O\rightarrow\text{ opposite side to}\theta \\ H\rightarrow\text{ hypotenuse} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} sin(45\degree)=\frac{5}{x} \\ \Rightarrow x=\frac{5}{sin(45\degree)}=\frac{5}{\frac{1}{\sqrt{2}}}=5\sqrt{2} \end{gathered}[/tex]Thus, the answer is x=5sqrt(2), the second optionThe Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected residents of certain county included 1400 who were over the age of 25, and 1120 of them were high school graduates.(a) Find the mean and standard deviation for the number of high school graduates in groups of 1400 Americans over the age of 25. Mean = Standard deviation =(b) Is that county result of 1120 unusually high, or low, or neither?
Is that county result of 1120 unusually high, low, or neither?
1148 - 2(14.37) = 1119.26
It is neither as it is within 2 standard deviation from the mean 1148.
Michael is constructing a boat ramp. He knows that the angle of elevation of the ramp is 30°. If the distance from the bottom of the boat ramp to the top of the boat ramp is 40 feet, what is the height of the boat ramp?
Let's draw a rough figure:
Here, h is the distance we are solving for.
Now,
With respect to the given angle 30 degrees, we have the hypotenuse and want to find the opposite side.
The trig ratio relating opposite side and hypotenuse is SINE.
Thus, we can write:
[tex]\sin (30)=\frac{opposite}{\text{hypotenuse}}=\frac{h}{40}[/tex]Cross multiiplying, we solve for h [remember, value of sin(30) is 1/2]:
[tex]\begin{gathered} \sin (30)=\frac{h}{40} \\ h=40\times\sin (30) \\ h=40\times\frac{1}{2} \\ h=20 \end{gathered}[/tex]The height of the boat ramp is 20 feet.
Every 3 months, homeowners in boice pay $46.00 for service provided by the city. how much do homeworkers pay in one year? (1 year = 12 months)
We were told that in every 3 months, homeowners in boice pay $46.00 for service provided by the city.
Given that there are 12 months in a year, the number of 3 months in a year would be
12/3 = 4
This means that $46 would be paid 4 times in a year.
Thus, the amount that the homeworkers would pay in a year is
4 * 46 = $184
Write a general formula to describe the variation. M varies directly with the square of d and inversely with the square root of x; M=12 when d=3 and x=4
Given that 'M' varies directly with the square of 'd',
[tex]M\propto d^2[/tex]Given that 'M' varies inversely with the square root of 'x',
[tex]M\propto\frac{1}{\sqrt[]{x}}[/tex]Combining the relationships,
[tex]M\propto\frac{d^2}{\sqrt[]{x}}[/tex]Let 'k' be the constant of proportionality. Then,
[tex]M=k\cdot\frac{d^2}{\sqrt[]{x}}[/tex]Given that M=12 when d=3 and x=4,
[tex]\begin{gathered} 12=k\cdot\frac{(3)^2}{\sqrt[]{4}} \\ 12=k\cdot\frac{9}{2} \\ k=\frac{12\cdot2}{9} \\ k=\frac{8}{3} \end{gathered}[/tex]Substitute the value of this constant in the general expression,
[tex]M=\frac{8}{3}\cdot\frac{d^2}{\sqrt[]{x}}[/tex]Thus, the required general formula to describe the relation is obtained as,
[tex]M=\frac{8}{3}\cdot\frac{d^2}{\sqrt[]{x}}[/tex]