7 copper spheres with radii of 4
inches are melted and formed into a
cube. How tall is the cube?
We will see that the cube must be 10.23 inches tall.
How tall is the cube?
The volume of the cube must be equal to the volume of the 4 spheres. Remember that the volume of a sphere of radius R is:
V = (4/3)*3.14*R^3
In this case, the radius is 4 inches, so we can write:
V = (4/3)*3.14*(4 in)^3 = 267.95 in^3
Then the volume of the 4 spheres is:
4*267.95 in^3 = 1,071.79 in^3
The volume of a cube of side length S is given by:
V = S^3
Then we must have:
S^3 = 1,071.79 in^3
S = ∛(1,071.79 in^3) = 10.23 in
We conclude that the cube is 10.23 inches tall.
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Question 8 (1 point) (04.03 MC) Calculate the area of triangle ABC with altitude CD, given A (-3,-4), B (-6,2), C (0,0), and D (-4,-2). Оа 14 square units Oь Ос 15 square units 18 square units Od 20 square units
Answer:
the answer is C
Step-by-step explanation:
HELP
The ceiling of Joey's living room is a square that is 22 ft long on each side. Joey knows the diagonal of the ceiling from corner to corner must be longer than 22 ft.
(a) he thinks that because a square cut and half forms a special right triangle the diagonal as the hypotenuse so he multiplies the side by 2 to get 44 ft what is Joey's mistake
(b) what is the correct length of the diagonal in Joey ceiling used to correct the special right triangles shortcut (give exact answer no rounding)
(c) used either the pythagorean theorem or the correct trigonometry ratios to solve for the length of the diagonal ( round to nearest tenth of a foot )
make sure to show all your work
I will report if you comment something random to just get points
Answer:
The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Let d represent the length of the diagonal, Usinng Pythagoras:
d² = 22² + 22²
d = 31 feet
Using trigonometric identity:
sin(45) = 22/d
d = 31 feet
The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.
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Step-by-step explanation:
Instructions: Write the equation of the line in Slope-Intercept Form
Answer:
y = -1/4x + 1
Step-by-step explanation:
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
The y-intercept of the line is 1, so in slope-intercept form, b will be 1.
Now, the line also intersects the y-axis at (4, 0). We can plug these two points into slope formula to find the slope: (0-1)/(4-0) = -1/4.
Therefore, the equation of the line is y=-1/4x + 1
I need help pls help pls help im writing this so this thing will stop bugging me to have a longer sentence
Answer:
The slope is 6
Step-by-step explanation:
m = y2 - y1/x2 - x1
ΔX = 3 – 2 = 1
ΔY = 7 – 1 = 6
6/1 = 6
Find the value of n.
Answer:
n=45
Step-by-step explanation:
Sum of interior angles can be calculated using formula: 180(number of sides - 2).
Hexagon has: 720 degrees. we subtract two right angles and get 4x=540. The x is the angle supplement to n. x=135 => 180-x=35 => n=45.
Jim drank 245 cups of orange juice and Jack drank 1110 cups less than Jim.
How much juice did jack drink? Explain your answer.
(i need a good explanation or i will get it wrong:(
Answer:
Step-by-step explanation:
Jim drank 2 and 4/5 orange juice
2and 4/5=14/5 orange juice
jack drank 1and 1/10 less than Jim= 11/10 less than Jim
I introduce the whole numbers into the fractions
we will convert the number 14/5 into a fraction that has the denominator 10, by multiplying by 2 both numerator and denominator
(14/5 )*2=28/10
Now we can find out how much juine Jack drank
28/10- 11/10= 17/10
so Jack drank 17/10 orange juice , the fraction can be written also as
1 and 7/10
Given the circle below with the secant FED and tangent CD, find the length of FE. Round to the nearest tenth if necessary.
The circle is an illustration of tangent and secant lines, and the length of FE in the circle is 9.3 units
How to determine the length FE?The lengths are given as:
DE = 12 unitsCD = 16 unitsStart calculating the length DF using:
DE * DF = CD²
So, we have:
12 * DF = 16²
Evaluate the exponent
12 * DF = 256
Divide both sides by 12
DF = 21.3
The length FE is then calculated using:
DF = FE + DE
Substitute DE = 12 and DF = 21.3
21.3 = FE + 12
Subtract 12 from both sides
FE = 21.3 - 12
Evaluate the difference
FE = 9.3
Hence, the length of FE in the circle is 9.3 units
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Tea Off served a total of 7,330 cups of chamomile tea to its customers last year. This year, the number
of served was 10% lower. How many cups of chamomile tea did the care serve this year?
Answer:
6,597 cups
Step-by-step explanation:
y=0.9x x=7,330 7,330 x 0.9= 6,597
HHHHHHHHHHHHHEEEELLLLLPPP MEEEEEE
After x-2y=8 is put in slope-intercept form, what are the slope and y-intercept?
A. m= -1/2 and b= 4
B. m= -2 and b= 8
C. m= 1/2 and b= -4
D. m= 2 and b= -8
Answer:
C. m=1/2 and b=-4
Step-by-step explanation:
To get the slope-intercept notation, you have to convert Ax+By = C to y = mx + b. We can do that by simply moving y to the left side and the rest to the right, or simply use the formula of m = -A/B, b = C/B
We'll do both, they're the same really.
x-2y=8
x-8=2y
2y=x - 8
y = 1/2*x - 4
Alternatively
x-2y=8
A = 1
B = -2
C = 8
m = -(1/-2) = 1/2
b = 8/-2 = -4
Solve for X:
Use the side-splitting theorem to solve for x.
If necessary, round your answer to the nearest tenth.
Answer:
x=13
Step-by-step explanation:
Side Splitter Theorem states that If a line is parallel to one side of a triangle and intersects the other two sides, it divides both sides proportionally.
21/14 =1.5
6x1.5 = 9
x-4=9
x=13
Find the measures of angles 1 and 2. If necessary, round to the tenths place. Hint: Do not assume that Point D is the center of the circle. A. mZ1 = 20° m2 = 20° B. m2 = 40° m2 = 140° C. ml = 82.5° mZ2 = 97.50 D. m1 = 97.5° m2 = 82.5°
Answer:
C. m<1 = 82.5 m<2 = 97.5
Step-by-step explanation:
Andrea spelled 18 out of 24 words correctly on a test. What percent of the words did
Andrea spell correctly?
Answer:
75%
Step-by-step explanation:
Find the next two terms in this sequence.
1,2,6,24,120, [??],[??]
Answer:
720, 5040
Step-by-step explanation:
It's always times plus 1. So,
1 x 2 = 2
2 x 3 = 6
6 x 4 = 24
24 x 5 = 120
120 x 6 = 720
720 x 7 = 5040
Countries that do not have enough resources to meet the needs of their population are said to be suffering from what?
A. Overpopulation
B. Urbanization
C. Pollution
D. Industrialization
Answer:
D. Industrialization cause of poverty.
Jonathan is building a box in the shape of a rectangular prism with
dimensions of inches by inches by inches. He plans to place a
diagonal brace inside the box from point to point . A diagram of
his box is shown.
The length of the diagonal brace when Jonathan is building a box in the shape of a rectangular prism is 17 inches.
How to calculate the length?From the information given, the dimensions are given as 8 inches by 12 inches by 9 inches.
Therefore, the length of the diagonal brace will be:
= ✓12 + ✓8 + ✓9
= ✓289
= 17
In conclusion, the correct option is 17 inches.
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Which is a valid sample of middle school students?
⚫️every tenth boy entering the school
⚫️every third student attending an after-school activity
⚫️every third student who enters each homeroom
⚫️every tenth person attending a school football game
Answer:
Every third student who enters each homeroom
Step-by-step explanation:
This would produce the least biased results as every third student gives a 3/x for students and there are y homerooms, giving the least biased results.
What is the slope of the line that passes through the points (6,2) and (-18, 2)?
Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
(x,y) slope is change in y / change in x⇒ Δy/Δx
(6,2)
(-18,2)
Δy = 2-2 = 0
Δx = 6-(-18) = 24
because the y values are the same, when you subtract you a slope of 0/24 or just 0 a horizontal line (because y is always =2)
Choose the factor pairs of 25.
1 and 25, 3 and 10, 5 and 6
1 and 25, 3 and 9
1 and 25, 2 and 11
1 and 25, 5 and 5
Answer:
1 and 25, 5 and 5
Step-by-step explanation:
because both 5×5=25 and 1×25=25 and 1×5=5 are all equal factor pairs of 25.
Question 15 of 20
A toy maker needs to put a rectangular piece in the side of a toy. He knows
from measuring that the top and bottom of the piece have a width of 4
inches. He also measured one length to be 3 inches. What is the length of the
last side?
A. 3 inches
B. 2 inches
C. 7 inches
D. 4 inches
Answer: 3 inches
Step-by-step explanation:
50 points each question. Please help. How do I solve?
[tex]I=\displaystyle \int \dfrac{\sqrt x}{\sqrt x -4} ~dx\\\\\text{Let,}\\\\~~~~u=\sqrt x-4\\\\\implies \dfrac{du}{dx} = \dfrac d{dx} \left( \sqrt x -4 \right)\\\\\implies \dfrac{du}{dx} = \dfrac 1{2 \sqrt x} \\\\\implies dx =2\sqrt x~ du\\\\\\I= \displaystyle \int \dfrac{u+4}{u+4 -4 } 2(u+4) du\\\\\\~~~=2\displaystyle \int \dfrac{(u+4)^2}{u} du\\\\\\~~~=2\displaystyle \int \dfrac{u^2+ 8u+16}{u} du\\\\\\~~~=2\displaystyle \int \left(u+8+\dfrac{16}u\right) du\\\\\\[/tex]
[tex]~~~=2\left(\displaystyle \int u ~ du + \displaystyle \int 8 ~ du + \displaystyle \int \dfrac{16} u ~ du\right) \\\\\\~~~=2\left( \dfrac {u^2}2 + 8u+16\ln |u| \right) +C\\\\\\~~~~= u^2 + 16u+ 32 \ln |u|+C\\\\\\~~~~=\left( \sqrt x -4 \right)^2 + 16\left( \sqrt x -4 \right) +32 \ln |\sqrt x -4|+C\\\\\\~~~~= x-8\sqrt x+16 +16\sqrt x -64 +32 \ln \left|\sqrt x-4 \right|+C\\\\\\\~~~~=x+8\sqrt x -48 +32\ln|\sqrt x -4| +C[/tex]
PLEASE HELP QUICKLY
The graph shows the relationship between the number of female eastern bluebirds observed by a biologist and the total number of eggs laid. Complete the given equation to show the relationship between b, the number of female eastern bluebirds observed, and t, the total number of eggs laid
The equation that models the number of female eastern bluebirds observed, b, and t, the total number of eggs laid is t = 5b
How to get the slope intercept form of a straight line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = mx +c
To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
Let we take:
b = the number of female eastern bluebirds observed
t = the total number of eggs laid
Since the relationship between b and t is forming a line, so it can be modeled by linear equation.
Here, we take 'b' as independent variable, and the value of 't' depending on the value of 'b', and therefore, let the linear equation representing them is:
[tex]t = mb + c[/tex]
For this case, we see that as the number of female eastern bluebird is increased by 1, half of 10 units (which is 5 units) is increased in the total number of eggs laid.
Thus, as we increase 'b' by 1 unit, there is increase by 5 units in the value of 't'.
and therefore, we get: m = increment in dependent variable per unit increment in independent variable = 5
Thus, the equation is:
[tex]t = 5b + c[/tex]
At b = 1, the number of eggs laid is 5, or t = 5, therefore, putting these values in the equation, we get:
[tex]5 = 5(1) = c\\c = 5-5=0[/tex]
Thus, the relation between t and b is t = 5b + 0= 5b
Thus, the equation that models the number of female eastern bluebirds observed, b, and t, the total number of eggs laid is t = 5b
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Luis has a bag that contains strawberry chews, apple chews, and peach chews. He performs an experiment. Luis randomly removes a chew from the bag, records the result, and returns the chew to the bag. Luis performs the experiment 37 times. The results are shown below:
A strawberry chew was selected 8 times.
A apple chew was selected 14 times.
A peach chew was selected 15 times.
Based on these results, express the probability that the next chew Luis removes from the bag will be a flavor other than strawberry as a fraction in simplest form.
The probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The number of times the experiment was done is 37 (15+14+8). The number of times apple chew came as a result of the experiment is 14, while the number of times peach chew came as a result of the experiment is 15. Therefore, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is
[tex]\rm Probability = \dfrac{\text{Number of times apple chew or peach chew was selected}}{\text{Total number of times experiment was performed}}\\\\\\Probability = \dfrac{14+15}{37} = \dfrac{29}{37}[/tex]
Hence, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).
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Help please!! MY LIFE DEPENDS ON THIS
Helium is a gas lighter than air that is used in balloons. The density of
helium is approximately 0.14 kilograms per cubic meter. You get 5 helium balloons for your 5th birthday, each with a volume of 14 cubic meters. How many kilograms of helium do the balloons contain, to the nearest hundredth?
Using proportions, given the density value, it is found that the ballons contain 9.8 kilograms of helium.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, we have that each ballon contain 0.14 kilograms per cubic meter.
You get 5 ballons, each with 14 cubic meters, hence the total volume is given by:
V = 5 x 14 = 70 m³.
Applying the density, we have that the total mass is given by:
M = 0.14 x 70 = 9.8 kilograms.
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The product of the ages of a man and his son is 160. In four years time, the man will be four times as old as his son. Find their ages.
Answer:
father = 32 s = 5 y/o
Step-by-step explanation:
f s = 160 ====> s = 160/f
f+4 = 4 ( s+4)
f + 4 = 4 (160/f +4)
f + 4 = 640/f + 16
f^2 + 4f = 640 + 16 f
f^2 -12f - 640 = 0 Use Quadratic formula to find f = 32 then s = 5
Let f(x)=2x-3 and g(x)=x+4. Find f(g(x)) and g(f(x)).
f(g(x)) =
Answer:
f(g(x)) = =2(-x^2+5)-3
=-2x^2+10-3
=-2x^2+7
Sorry, I'm not sure about g(f(x)).
Step-by-step explanation:
f(g(x))=f(-x^2+5)=2x-3
=2(-x^2+5)-3
=-2x^2+10-3
=-2x^2+7
PLEASE HELP! Need answer fast
Answer:
B.
Step-by-step explanation:
Because if you look closely you will be able to tell which answer it is by looking at the way the shape formed andjust breakaprt the shape .
Question 10
Graph g(x) =
Y
<
- 4(x - 2)² + 4.
10-9-8-7 -6 -5 -4 -3 -2 -1
-2
-3
-4
-5
-6
-7
-8
-9
10
Clear All Draw:
ZAV
Question Help: Video
Add Work
>
10+
9
8
7-
6
S
4
3
2
21
1 2 3 4 5 6 7 8 9 10
Answer:
2?
Step-by-step explanation:
A pet store has 150
150
goldfish and betta fish altogether.
The ratio of goldfish to betta fish is 2:3
2:3
.
How many goldfish does the pet store have?
CLEAR CHECK
What fraction of the fish are goldfish?
How many goldfish does the pet store have? goldfish
Answer:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEStep-by-step explanation:
Let the goldfish be G.
• Let the betta fish be B.
Given the following data:
• Total number of fishes = 150 fishes.
• Ratio of G to B = 2:3
• Total ratio= 2 + 3 = 5
To calculate the number of goldfish that the pet store have:
What is ratio?
Ratio can be defined as an expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
Mathematically, the number of goldfish in the pet store is given by this expression:
2 G = x 150 5
G = 0.4 x 150
G = 60 fishes.