Answer:
The distance from the Zoo to the city is 80 km
Step-by-step explanation:
The given information are;
The speed of the tour bus = 78 km/h
The point of passing the tour bus = Half way between the city and the Zoo
The time taken after passing the tour bus when it was still 14 km from the city = 20 minutes = 20/60 hour = 1/3 hour
Therefore, we have that the distance covered by the tour bus in 1/3 hour = Time ×Speed = 1/3×78 = 26 km
The distance remaining for the tour bus to reach the city = 14 km
The total distance from the time of observation of the tour bus = Half the distance from the city to the Zoo
Also, the total distance from the time of observation of the tour bus = 26 km + 14 km = 40 km
∴ 40 km = Half the distance from the city to the Zoo
Which gives;
The distance from the Zoo to the city = 2 × 40 km = 80 km.
Orion is working with a data set that compares the outside temperature, in degrees Celsius, to the number of gallons of ice cream sold per day at a local grocery store.
The data has a line of best fit modeled by the function f(x) = 3x + 4 . Orion determines that when the temperature is 25∘C, the store should sell about 79 gallons of ice cream. The correlation coefficient of the data is 0.39.
Explain how accurate Orion expects the prediction to be.
Answer: kindly check Explanation.
Step-by-step explanation:
The function f(x) = 3x + 4 is a linear regression model. Orion's prediction was obtained by Substituting 25 for x to obtain the predicted variable
f(25) = 3(25) + 4 = 75 + 4 = 79.
However, with a correlation Coefficient of 0.39, which is a numerical value of range - 1 to +1 and is used to measure the statistical relationship between the dependent variable (number of gallons of ice-cream sold per day) and the independent variable (temperature).
The closer the correlation Coefficient (r) value is to +1 or - 1, the stronger the degree of correlation. Positive r values depicts positive relationship while negative r values depicts negative relationship. The closer the r value is to 0. The weaker the relationship and a r value of means there is no Relationship exists between the two variables.
With a correlation Coefficient of 0.39, we can Infer that that only a moderate positive relationship exists between temperature and gallons of ice cream sold per day.
Write an equation in slope-intercept form of the line that passes through (-3,3) and (1,2)
Answer:
y = -1/4x + 9/4
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
3-2/-3-1
Slope = [tex]-\frac{1}{4}[/tex]
In this problem, to find the y-intercept [tex]y-y_1 = m (x-x_1)\\[/tex].
y-3 = -1/4 (x+3)
y= -1/4x + 9/4
Answer:
yoo
Step-by-step explanation:
I am being timed pls asap
Answer:
Writing it in matrix form
- 2 - 4 - 5 - 155
1 1 6 101
2 2 - 3 37
I hope this helps you
The volume of a right circular cone with both
2507
diameter and height equal to his What is the
3
value of h?
A) 5
B) 10
C) 20
D) 40
Question:
The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.
What is the value of h?
Answer:
A. 5
Step-by-step explanation:
Given
Solid Shape: Cone
Volume = 250/7
Diameter = Height
Required
Find the height of the cone
Provided that the diameter (D) and the height (h) are equal; This implies that
D = h ------ (1)
Also, Diameter (D) = 2 * Radius (r)
D = 2r
Substitute 2r for D in (1)
2r = h
Multiply both sides by ½
½ * 2r = ½ * h
r = ½h
Volume of a cone is calculated by;
Volume = ⅓πr²h
⅓πr²h = 250/7
Substitute ½h for r
[tex]\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]
Take π as 22/7, the expression becomes
[tex]\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]
Open the bracket
[tex]\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}[/tex]
Multiply both sides by 7
[tex]7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7[/tex]
[tex]\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250[/tex]
Multiply both sides by 3
[tex]3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3[/tex]
[tex]22 * \frac{1}{4}h^2 * h = 750[/tex]
Multiply both sides by 4
[tex]4 * 22 * \frac{1}{4}h^2 * h = 750 * 4[/tex]
[tex]22 * h^2 * h = 3000[/tex]
[tex]22 * h^3 = 3000[/tex]
Divide both sides by 22
[tex]h^3 = \frac{3000}{22}[/tex]
[tex]h^3 = 136.36[/tex]
Take cube root of both sides
[tex]h = \sqrt[3]{136.36}[/tex]
[tex]h = 5.15[/tex]
[tex]h = 5[/tex] (Approximated)
Last year, 1,345 bicyclists showed up to the bicycle race. This year, only 690 bicyclists showed up. Write the ratio of the number of bicyclists that showed up to the bicycle race for the past two years.
Answer:
138 : 269
Step-by-step explanation:
Last year, the number of bicyclists that showed up was 1345.
This year, there were 690 bicyclists.
The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:
690 : 1345
Let us put it in simplest terms:
138 : 269
pleaseeeeeeeeeeeeeee hellllllllllllp pleaseeeeee helpppppp
The tables for f(x) and g(x) are shown below.
х
f(x)
-11
-5
-2
1
1
13
5
29
х
-5
g(x)
-7
-1
-2
1
5
5
13
What is the value of (f-9)(5)?
Answer:
16
Step-by-step explanation:
(f - g)(5) = f(5) -g(5)
From the tables, ...
f(5) = 29
g(5) = 13
Your desired function is ...
f(5) -g(5) = 29 -13 = 16
Please answer this question now
Answer:
m < S = 55°
Step-by-step explanation:
Based on tangent theorem, a tangent line is said to be perpendicular to a radius of a circle when they intercept. The point at which they meet is said to be at 90°.
Therefore, in the ∆PQS, given, m < P = 90°.
m < Q = 35°
m < S = 180° - (90° + 35°) (sum of the angles in a triangle)
m < S = 180° - 125°
m < S = 55°
If f(x) =x/2+8, what is f(x) when x=10
Answer:
f(10) =13
Step-by-step explanation:
f(x) =x/2+8,
Let x = 10
f(10) =10/2+8,
= 5+8
= 13
Q3. Ishah spins a fair 5-sided spinner. She then throws a fair coin.
(i) List all the possible outcomes she could get. The first one has been done for you.
(1, H)
(ii) Ishah spins the spinner and tosses the coin.
Work out the probability that she will get a 2 and a head.
Answer:
see below
Step-by-step explanation:
1.
1, H - 2, H - 3, H - 4, H - 5, H
1, T - 2, T - 3, T - 4, T - 5, T
2.
2,H is one out of 10 possible outcomes, so the probability is 1/10
The Goodsmell perfume producing company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to hold at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and he corresponding surface are and volume.
Answer:
Dimensions of the bottle
x (radius of the base ) = 3,99 cm
h (heigh of the bottle ) = 3,99 cm
Surface area = 149,99 cm²
Volume of the bottle = 199,45 cm³
Step-by-step explanation:
The bottle volume must be V(b) = 100 ml or V(b) = 100 cm³
The shape of the bottle is cylindrical
Surface area of bottle is
S = surface area of the base + lateral area
Area of the base = π*x ² where x is radius of circle
Lateral area is 2*π*x*h where h is the heigh of the bottle
V(b) = π* x²*h (1)
π*x² + 2*π*x*h < 150 cm² we work with the limit 150
π*x² + 2*π*x*h = 150
h = (150 - π*x²) /2*x*π
Plugging that value in equation (1)
V(x) = π*x² * (150 - π*x²) /2*x*π ⇒ V(x) = 150*π*x²/2*x*π - π²*x⁴/2*x*π
V(x) = 75*x - π*x³/2
Taking derivatives on both sides of the equation
V´(x) = 75 - 3*π*x²/2
V´(x) = 0 75 - 3*π*x² /2 = 0
x² = 75*2 /3*π ⇒ x² = 15,92 ⇒ x = 3,99 cm
And h = ( 150 -π*x² )/2*π*x
h = ( 150 - 49,98 )/25,05
h = 3,99 cm
Dimensions of the bottle
x (radius of the base ) = 3,99 cm
h (heigh of the bottle ) = 3,99 cm
Surface area = 149,99 cm²
Volume of the bottle = 199,45 cm³
Anya graphed the line (y−2)=3(x−1) on the coordinate grid. A coordinate plane with a line passing through the points, (negative 2, negative 7), (0, negative 1), and (1, 2). What is the slope of Anya’s line? −3 −1 1 3
Answer:
Slope of Anya's line is m = 3
Step-by-step explanation:
Explanation:-
Given Anya graphed the line
(y−2)=3(x−1)
we know that slope intercept form is
y = mx +c
now given Anya line
y−2=3(x−1)
⇒ y - 2 = 3x - 3
⇒ y = 3x - 3 + 2
⇒ y = 3 x - 1
Comparing slope -intercept form
y = mx +c
slope of Anya's line is m = 3 and y-intercept C = -1
Answer:
M=3
Step-by-step explanation:
Hope this helps!
Q2.
If ε={1, 2, 3, 4,………….., 10} and
A = Set of even numbers between 1 and 10.
B = Set of odd numbers between 1 and 10
C = Set of prime numbers between 1 and 10
(i)
List down the elements of sets A, B and C.
(ii)
List down the number of elements in sets A, B and C.
(iii)
Find AUC.
(iv)
Find BC.
(v)
Find AC
Answer:
hope its helpful to uh....
What are the roots of the function y = 4x2 + 2x - 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x - 30.
Factor out the GCF of
Next, factor the trinomial completely. The equation becomes
Use the zero product property and set each factor equal to zero and solve.
The roots of the function are
Answer:
-3, 5/2
Step-by-step explanation:
What are the roots of the function y = 4x2 + 2x – 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)
Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)
Use the zero product property and set each factor equal to zero and solve.
x+3=0 2x-5 = 0
x = -3, 5/2
The roots of the function are -3, 5/2.
Hope this helped!
The roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
y = 4x² + 2x - 30
To find the roots of the quadratic equation plug y = 0
4x² + 2x - 30 = 0
4x² + 12x - 10x - 30 = 0
4x(x + 3) - 10(x + 3) = 0
(x + 3)(4x -10) = 0
x + 3 = 0 or 4x - 10 = 0
x = -3 or x = 10/4 = 5/2
Thus, the roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
Eldrick is using the dot plots to compare two sets of data. Both plots use the same number line. What is the difference between the mean of each data set?
Answer:
15
Step-by-step explanation:
mean means add all the numbers and divide them by how many there are
plot 1: 63 divided by 9 equals 7
plot 2: 330 divided by 15 equals 22
so now we need to subtract 22 minus 7 equals 15
hope this helps
Answer:
15
Step-by-step explanation: you have to add all of the numbers and then divide the answer by the number of numers you added
Which shows how to find the y-coordinate of the point that will divide CD into a 5:2 ratio using the formula y = (y2 – y1) + y1? y = (3 – 1) + 1 y = (3 + 4) – 4 y = (3 – 1) + 1 y = (3 + 4) – 4
Answer:
[tex]\frac{5}{5+2}(3-1)+ 1[/tex]
Step-by-step explanation:
To find the coordinate of the point that divides a line segment AB with point A at ([tex]x_1,y_1[/tex]) and point B at [tex](x_2,y_2)[/tex] in the proportion c:d, the formula used to find the location of the point is:
[tex]x-coordinate:\\\frac{c}{c+d}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{c}{c+d}(y_2-y_1)+y_1[/tex]
Therefore the y coordinate that divides line segment CD with point C at ([tex]-4,1[/tex]) and point D at [tex](3,3)[/tex] in the proportion 5:2 is given by:
[tex]for\ y-coordinate:\\\frac{c}{c+d}(y_2-y_1)+y_1\\=\frac{5}{5+2}(3-1)+ 1\\=\frac{5}{7}(2)+1=\frac{17}{7}[/tex]
Answer:
{5/7}(3-1)+1
Step-by-step explanation:
HELP - 100 POINTS AND BRAINLIEST!! Find the area and volume - a square has a side length of 6.25 Please show your work! Thank you!
Step-by-step explanation:
Area: bh
The shape is a square in which the side lengths are the same, so we multiply the number squared.
A = 6.25(6.25)
A = 39.06
Volume: lwh
6.25^3 = V
V = 244.14
Hope this helps:)
Step-by-step explanation:
Area: bh
The shape is a square in which the side lengths are the same, so we multiply the number squared.
A = 6.25(6.25)
A = 39.06
Volume: lwh
6.25^3 = V
V = 244.14
I hope I contributed
If f(x) = 3x - 5 and g(x) = 7x + 2, what is f(x) x g(x)
Answer:
21x + 1
Step-by-step explanation:
f[g(x)]
= f(7x + 2)
= 3(7x + 2) - 5
= 21x + 6 - 5
= 21x + 1
the length f a rectangle is 3 ties its width, the perimeter of it is 24cm. what is the area of it?
Answer: 27cm²
Step-by-step explanation:
lets take the width as x and length as 3x( since length is 3 times the width)…
Perimeter of the rectangle is 24 cm( 2*(l+b))= 2×(3x+x):24
2×4x=24
8x=24
X( width): 24/8=3cm
Length= 3x: 3*3=9cm
Area of the rectangle: ( l*w)= 9×3: 27cm²
Answer:
Step-by-step explanation:
What is the y-coordinate of point D after a translation of
(x, y) - (x + 6,7 - 4)?
Hey There!!
Your answer will be 1.
Step-by-step explanation:
If the coordinates of the point D' are (x, y), then, after translation, it will be
D(x + 6, y - 4).
that is 6 units right and 4 units down
It is given that the point before translation is D'(3, 5).
So, x + 6 = 3 + 6 = 9 and
y - 4 = 5 - 4 = 1
So, the y coordinate of point D after translation is 1.
Hope This Helps!!!
By ♡Itsbrazts♡
HELP ASAP, PLEASE!!!!
Answer:
Fraction = 5/10 = 1/2
Decimal = 0.5
Step-by-step explanation:
Answer:
fraction-5/10 decimal-0.5
plz give brainiest
Step-by-step explanation:
In ΔABC, if AB = 10 and BC = 6, AC can NOT be equal to
A. 4
B. 6
C. 8
D. 10
Answer:
A
Step-by-step explanation:
The answer is A because in the triangle, the two smaller sides added up have to be more than the bigger side, or equal, if it is a right triangle. so 4 is the smallest 4+6=10, so it does not work, but lets see if it is a right triangle
4^2+6^2=16+36=52. it would have to equal 100 to be a right triangle. Use Pythagorean thereon.
For a triangle, the any two sides must be greater than the third side.The measure of AC cannot be equal to 4
What is a triangle?A triangle has three sides and angle. For a triangle, the any two sides must be greater than the third side.
Given the following parameters
AB = 10 and
BC = 6
The measure of AC must be 8 for the theorem above to be true
6 +8 > 10
6 +10 > 8
10 + 8 > 6
Hence the measure of AC cannot be equal to 4
Learn more on triangles here: https://brainly.com/question/23945265
#SPJ6
PLEASE HELP IMMEDIATELY
Find x when[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
[tex] - \frac{23}{4} [/tex]
[tex] - \frac{19}{4} [/tex]
[tex] \frac{19}{4} [/tex]
[tex] \frac{23}{4} [/tex]
Answer:
[tex]x = - \frac{19}{4} [/tex]Option B is the correct option.
Step-by-step explanation:
[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
Move constant to R.H.S and change its sign:
[tex]x = - \frac{21}{4} + \frac{1}{2} [/tex]
Take the L.C.M
[tex]x = \frac{ - 21 + 1 \times 2}{4} [/tex]
[tex]x = \frac{ - 21 + 2}{4} [/tex]
Calculate
[tex]x = - \frac{19}{4} [/tex]
Hope this helps...
Good luck on your assignment..
Step-by-step explanation:
-19/4 is the correct answer for your question
Built in 2011, the capital gate tower is 150 meters tall (measured vertically from the ground) and makes a 72 degree angle with the ground. If you were to climb to the top and then accidentally drop your keys, how far from the base of the tower would they land?
Answer:
Step-by-step explanation:
You can create a right triangle out of this information and then use right triangle trig to solve.
We are given the height of the triangle as the height of the tower which is 150m.
We are given the angle of inclination as the degree the tower makes with the ground which is 72.
From the angle of 72 degrees, which is also known as the reference angle, we have the side across from it (the height) and we are looking for the side adjacent to it (how far from the base of the tower the keys will land). Side opposite the reference angle over side adjacent to the reference angle is the tangent ratio:
[tex]tan(72)=\frac{150}{x}[/tex] and, solving for x,
[tex]x=\frac{150}{tan(72)}[/tex]
Make sure your calculator is in degree mode to solve this. Divide 150 by the tan(72) and find that
x = 48.7 m
How many ways are possible to choose 3 days out of February? NOTE: Use 28 days for the number of days in February. A) 3276 B) 378 C) 20475 D) 2925
Answer:
A) 3,276 ways.
Step-by-step explanation:
In this case, choosing February 1, February 12, and February 20 would be the same thing as choosing February 12, February 1, and February 20. So, since order does not matter, we will use a combination to solve the question.
The formula for combinations is...
n! / [r!(n - r)!], where n = the number of days in February (28) and r = the number of days you are choosing (3).
28! / [3! * (28 - 3)!]
= 28! / (6 * 25!)
= (28 * 27 * 26) / 6
= (14 * 9 * 26) / 1
= 14 * 9 * 26
= 126 * 26
= A) 3,276.
Hope this helps!
Priscilla has three cups of apples left. She wants to use them in another fruit salad.
How would she find out how much of the other fruits she needs to use up the
remaining apples?
Answer:
To use up the remaining 3cups of apples, she would need 3cups of oranges, 12cups of strawberries, 6cups of cherry and 9 cups of grape.
Step-by-step explanation:
This is a continuation of the question on the recipe for making salad. The initial recipe from her grandmother is stated below (found on brainly, ID 6786167).
The fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry, and three parts grape.
Priscilla uses the same measuring cup to measure all of the fruit, so one part is equal to one cup of diced fruit.
Number of cups required for each fruit in the original recipe:
apple = 1 cup , orange = 1 cup, strawberry = 4cups, cherry = 2cups, grape = 3cups
Original ratios of the cup of fruit respectively = 1:1:4:2:3
Total number of cups required in the original recipe: 1+1+4+2+3 = 11 cups
Now for this question, 3 cups of apples are remaining. And we want to find number of other fruits she needs in order to use up the remaining apples.
To do this we would use the ratios of the cup of fruit.
When we had 1 apple, the ratio was = 1
Now we have 3apples, the new ratio = 3×original ratio
=3×1 = 3
This means we would multiply each of the fruit ratios by 3
For orange, new ratio = 3×1 = 3
For strawberries, new ratio = 3×4 = 12
For cherry, new ratio = 3×2 = 6
For grape, new ratio = 3×3 = 9
To use up the remaining 3cups of apples, she would need 3cups of oranges, 12cups of strawberries, 6cups of cherry and 9 cups of grape.
Answer:
Priscilla uses one part orange, four parts strawberry, two parts cherry, and three parts grape for every one part apple. So, to use three times the quantity of apples, she will have to use three times the quantity of the other fruits as well. She needs three parts orange, twelve parts strawberry, six parts cherry, and nine parts grape for three parts apple.
Step-by-step explanation:
plato/edmentum answer
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number. Also, If the tens digit is x, then the equation is: ___?
how do u find rate of change on a graph
Step-by-step explanation:
The correct answer is the vertical change divided by the horizontal change between two points on a line. We can find the slope of a line on a graph by counting off the rise and the run between two points. If a line rises 4 units for every 1 unit that it runs, the slope is 4 divided by 1, or 4.
Answer:
Calculate the rise over the run/the change in y over the change in x
Step-by-step explanation:
In order to find the rate of change on a graph from a slope, you need to look at how many units up and how many units to the right. Find a solid point on the graph for both the x and y directions. Count how many units go up and how many go right. Divide how many units go up by how many go to the right and that is the rate of change on the graph.
You are remodeling your kitchen. You've contacted two tiling companies who
gladly told you how long it took their workers to tile a floor of a similar size.
Jim completed half the floor in 12 hours. Pete completed the other half of the
floor in 10 hours. If Pete can lay 25 more tiles per hour than Jim, what
equation would you use to find the rate that Jim can lay tiles? Let x represent
Jim's rate.
Answer:
12x=10(25+x)
Step-by-step explanation:
Jim's rate=x
Pete's rate=y
Jim and Pete lays the same number of tiles.
So we have,
12x=10y
Pete's can lay 25 more tiles than Jim per hour
We have
y=25+x
Substitute y=25+x into 12x=10y
12x=10y
12x=10(25+x)
12x=250+10x
12x-10x=250
2x=250
x=250/2
=125
x=125
12x=10(25+x) is the equation used to find the rate that Jim can lay tiles
Given: x + 2y=-6.
Solve for y
Oy=x-6/2
Oy=-x+6/2
Oy=-x-6/2
Answer:
y = (-x - 6)/2
Step-by-step explanation:
x + 2y = -6
2y = -x - 6
y = (-x - 6)/2