[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\implies \stackrel{\textit{8\% of (s)ales}}{\left(\cfrac{8}{100} \right)s}\qquad \qquad \begin{cases} c=commission\\ s=total~sales \end{cases}[/tex]
[tex]\bf \stackrel{\textit{her (c)ommision is 8\% of (s)ales}}{c = \cfrac{8}{100}s\implies c=\cfrac{8s}{100}}\implies \stackrel{\textit{we know she made 2560 in commision}}{2560=\cfrac{8s}{100}\implies 256000=8s} \\\\\\ \cfrac{256000}{8}=s\implies 32000=s[/tex]
A bird caught a fish on the waters surface and flew in a straight line diagonal to the water for 100 yards. Then, it dropped the fish straight down. The fish landed at a spot 50 yards away horizontally from the point where the bird caught it.
Select the correct answers.
The bird flies at an angle of 1. ______ degrees from the water, and its height from the ground when it drops the fish is 2. _____ yards.
Blank 1 choices:
A) 30
B) 60
C) 78.7
Blank 2 choices:
A) 8.6
B) 86.6
C) 111.8
Random answers will be reported!
Answer:
1. B
2. B
Step-by-step explanation:
** Attached picture of the situation
The bird caught the fish at point A, flew until B (which is 100 yds away, dropped the fish at C (which is horizontally 50 yards from A).
1.
We want the angle that the bird creates with the water (horizontal). It is angle BAC. With respect to the right triangle, we can say that we know "hypotenuse" and "adjacent" side to angle BAC. cosine relates hypotenuse and adjacent, thus we can write:
[tex]Cos(BAC)=\frac{50}{100}\\Cos(BAC)=\frac{1}{2}\\BAC=Cos^{-1}(\frac{1}{2})\\BAC=60[/tex]
correct answer is B
2.
Here, we want to find the distance (length) of segment BC. With respect to the angle BAC (we found to be 60), we can say BC is "opposite". We know hypotenuse to be 100. So let's use sine, since sine is ratio of opposite to hypotenuse. Thus, we can write:
[tex]Sin(BAC)=\frac{BC}{100}\\Sin(60)=\frac{BC}{100}\\BC=Sin(60)*100\\BC=86.6[/tex]
correct answer is B
The answers should be B)60 and B) 86.6
PLZ HURRY IT'S URGENT!!!
Use graph paper and a straightedge to draw the figure. The set of points (2, 4), (5, 8), (11, 8), and (8, 4) identifies the vertices of a quadrilateral. Which is the most specific description to tell which figure the points form? A. parallelogram B. square C. rectangle D. rhombus
Answer:
Parallelogram
Step-by-step explanation:
graphing them makes two sets of parallel lines
Find f(-5)
f(x) = -4x + 3
For this case we have a function of the form[tex]y = f (x)[/tex]
Where:
[tex]f (x) = - 4x + 3[/tex]
We must find the value of the function when the variable x is -5.
Then, substituting, [tex]x = -5[/tex]
[tex]f (-5) = - 4 (-5) +3[/tex]
We have that by sign law[tex]- * - = +[/tex]
[tex]f (-5) = 20 + 3\\f (-5) = 23[/tex]
Answer:
[tex]f (-5) = 23[/tex]
ANSWER
[tex]f( - 5)=23[/tex]
EXPLANATION
The given function is
[tex]f(x)=-4x+3[/tex]
To find f(-5), we substitute x=-5 to obtain;
[tex]f( - 5)=-4( - 5)+3[/tex]
We multiply out to obtain:
[tex]f( - 5)=20+3[/tex]
We simplify to get,
[tex]f( - 5)=23[/tex]
The volume of a cylinder is 4,320π ft3. The diameter is 24 ft. What is the height of the cylinder?
ANSWER
The height is 30 feet
EXPLANATION
The volume of a cylinder is calculated using the formula;
[tex]V = \pi {r}^{2} h[/tex]
The diameter is 24 ft. This implies that the radius of the cylinder is 12ft.
We substitute known values to get:
[tex]4320\pi= \pi{(12)}^{2} h[/tex]
[tex]4320\pi=144 \pi h[/tex]
Divide both sides by 144π
[tex]h = 30ft[/tex]
find a non-zero value of K such that kx^2+ 8x+8+= 0 has only one solution. What is the solution?
kx² + 8x + 8 = 0
We want this to have just one solution, we know this equation:
x = (-b ± √Δ)/2a
So if Δ = 0 we have just one solution.
Δ = b² - 4.a.c
0 = 8² - 4.k.8
0 = 64 - 32k
32k = 64
k = 2
2x² + 8x + 8 = 0
x² + 4x + 4 = 0
(x + 2)² = 0
x + 2 = 0
x = -2
The solution is -2.
The non-zero value of k for which the quadratic equation kx²+8x+8=0 has only one solution is '1'. This is arrived at by setting the discriminant of the quadratic equation (b² - 4ac) to zero and solving for 'k.'
Explanation:The subject of this question is a mathematical concept known as a discriminant in a quadratic equation. A quadratic equation is generally in the form of ax²+bx+c = 0. The discriminant of the quadratic equation kx²+8x+8=0 is given by the formula b²-4ac, where 'a is the coefficient of x² (which is 'k' in this case), 'b' is the coefficient of x, and 'c' is the constant term. The discriminant must equal zero for the quadratic equation to have only one solution. Therefore, we have 8² - 4*k*8 = 0. Solving this equation gives k = 1, which is a non-zero value.
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If 30 Coins In Quarters And Dimes Are Worth $4.80, How Many Of Each Coin Are There?
Answer:
There are 18 dimes and 12 quarters
Step-by-step explanation:
Remember that
1 Dime =$0.10
1 Quarter=$0.25
Let
x-----> the number of dimes
y-----> the number of quarters
we know that
x+y=30
x=30-y ------> equation A
0.10x+0.25y=4.80
Multiply by 100 both sides
10x+25y=480 ------> equation B
Substitute equation A in equation B and solve for y
10(30-y)+25y=480
300-10y+25y=480
15y=180
y=12 quarters
Find the value of x
x=30-y=30-12=18 dimes
therefore
There are 18 dimes and 12 quarters
Final answer:
To solve this problem, set up a system of equations and solve them simultaneously.
Explanation:
Let's solve this problem using a system of equations.
Let's assume that the number of quarters is 'x' and the number of dimes is 'y'.
We can set up two equations based on the given information:
Equation 1: x + y = 30 (since there are 30 coins in total)Equation 2: 0.25x + 0.10y = 4.80 (since the total value of the coins is $4.80)Solving these equations simultaneously, we can find the values of 'x' and 'y', which represent the number of quarters and dimes respectively.
By substituting the value of x from Equation 1 into Equation 2, we get:
0.25(30 - y) + 0.10y = 4.80
7.50 - 0.25y + 0.10y = 4.80
-0.15y = -2.70
y = 18
Substituting the value of y into Equation 1, we get:
x + 18 = 30
x = 12
Therefore, there are 12 quarters and 18 dimes.
debbie rode her bicycle 12 miles every day for 5 months. there were 153 days in these 5 months how many miles did she ride
She rode 1,836 miles in total.
Andria is conducting an experiment to determine whether a new medication is effective in reducing swelling. She gets 1,000 volunteers with swelling and divides them into 2 groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of swelling. What can Andria conclude from this experiment?
Answer:
The medicine treats swelling
Step-by-step explanation:
"The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of swelling. What can Andria conclude from this experiment?"
If she does not give placebo, which she should, then we can only conclude that the medication might be effective. Might, because the thought of the medicine fixing swelling might actually be what helps them.
This takes us to the next topic- placebo experiments.
Most good experiments, to elaborate, are "double blind," one group receives a placebo, and another the medication, and neither know which.
In this case, assuming that the placebo was ineffective, we can conclude that the medicine is effective in treating swelling.
what are the values of a and b
Answer:
[tex]\large\boxed{B.\ a=8,\ b=4\sqrt5}[/tex]
Step-by-step explanation:
We have three similar triangles:
[tex]\triangle ABC\sim\triangle DBA\sim\triangle DAC[/tex]
therefore the sides are in proportion:
[tex]\dfrac{AD}{CD}=\dfrac{BD}{AD}[/tex]
We have AD = a, CD = 16 and BD = 4. Substitute:
[tex]\dfrac{a}{16}=\dfrac{4}{a}[/tex] cross multiply
[tex](a)(a)=(16)(4)\\\\a^2=64\to a=\sqrt{64}\\\\a=8[/tex]
and other proportion:
[tex]\dfrac{AB}{BC}=\dfrac{BD}{AB}[/tex]
We have AB = b, BC = 16 + 4 = 20 and BD = 4. Substitute:
[tex]\dfrac{b}{20}=\dfrac{4}{b}[/tex] cross multiply
[tex](b)(b)=(20)(4)\\\\b^2=80\to b=\sqrt{80}\\\\b=\sqrt{16\cdot5}\\\\b=\sqrt{16}\cdot\sqrt{5}\\\\b=4\sqrt{5}[/tex]
Option B is the correct option.
Similarity of two triangles,
Condition for the similarity of two triangles,
"If two triangles are similar, corresponding sides of these triangles will be proportional"
From the picture attached,
ΔADC and ΔBDA are similar,
By the condition of the similarity, corresponding sides will be proportional.
[tex]\frac{DA}{BD}= \frac{DC}{DA}= \frac{AC}{BA}[/tex]
Substitute the measures given in the picture,
[tex]\frac{a}{4}= \frac{16}{a}= \frac{AC}{b}[/tex]
[tex]\frac{a}{4}=\frac{16}{a}[/tex]
[tex]a^2=64[/tex]
[tex]a=8[/tex]
Now apply Pythagoras theorem in ΔADB,
AB² = AD² + DB²
b² = a² + 4²
b² = 8² + 4² [Since, a = 8]
b = √80
b = 4√5
Therefore, Option B will be the correct option.
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Please help with this quiz question!
Using the parallelogram pictured, find the length of the shorter diagonal. Round your answer to the nearest inch.
A) 32.1 in
B) 31.0 in
C) 22.3 in
D) 21.0 in
According to google your answer is c
What is the Value of x
Answer:27
Step-by-step explanation:26/18=39/×
26x=702
×=27
Check the picture below.
Jennifer has 5/6 of a candy. At and would like to split it equally between herself and her 4 friends. What fraction of the candy bar will each person get?
Answer:
1/6
Step-by-step explanation:
Candy = 5/6
5 people = 5/6
1 person
= 5/6 ÷ 5
= 5/6 x 1/5
= 1/6
Answer:
1/6
Step-by-step explanation:
The volume of the rectangular solid is _____ cubic inches
Answer:
45 cubic inches
I hope this helped you : )
Step-by-step explanation:
To find the volume you must use the formula ( Volume = Length x Width x Height)
So, ( 5 x 3 x 3 = 45)
45 cubic inches, it’s just l*w*h
How to find the surface area of a box and the volume?
for surface area you find the area of a square face (11*9=99) but there are 2 square faces so it would be 2 lots of 99 (99*2=198)
then you find the area of the rectangle faces (12*9=108)
there are 4 rectangle faces so you would do 108*4=432
then just do 432 + 198 =630
so surface area is 630
for volume you do b*l*h
so just do 11*9*12
= 1188
so volume is 1188cm^3
Find the surface area of the prism. Write your answer as fraction or mixed number.
Answer:
From the measure the picture provides us, we can conclude that the prism is a cube, which also tells us that all 6 sides of this prism have equal surface area, so we only need to calculate one of them and multiply the result by 6:
The surface area of one side of the cube should be: 2/3 . 2/3 = 4/9 (ft²)
The surface area of the prism should be: 4/9 . 6 = 24/9 = 8/3 (ft²)
A prism is a polyhedron composed of an n-sided polygon basis. The surface area of the prism is 8/3 ft².
What is a prism?A prism is a polyhedron composed of an n-sided polygon basis, a second base that is a translated duplicate of the first, and n additional faces, all of which must be parallelograms, connecting the two bases. All parallel cross-sections to the bases are translations of the bases.
Given the length of the side is 2/3 ft. Therefore, the surface area of the given prism can be written as,
The surface area of the prism = 6s² = 6(2/3)² ft² = 8/3 ft²
Hence, the surface area of the prism is 8/3 ft².
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What’s 3.24 rounded to the nearest tenth
Answer:
3.2 is the corrext amswr
Step-by-step explanation:
The answer is 3.2 because you only round up if it’s .5 or higher and round down if it’s .4 or lower
15 pts
what is the total volume of juice in a six-pack if each can is 6 inches tall and has a diameter of 3 inches? 42.39in^3 or 254.3in^3
please show your work and answer it correctly
Answer:
The total volume of juice in a six-pack is [tex]254.3\ in^{2}[/tex]
Step-by-step explanation:
step 1
Find the volume of one can
The volume of the cylinder (can of juice) is
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter
[tex]h=6\ in[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=(3.14)(1.5)^{2} (6)[/tex]
[tex]V=42.39\ in^{2}[/tex]
step 2
Find the total volume of juice in a six-pack
Multiply the volume of one can by 6
[tex]42.39*(6)=254.3\ in^{2}[/tex]
The total volume of juice in a six-pack where each can is 6 inches tall and has a diameter of 3 inches is calculated using the volume of a cylinder formula. The total volume is 254.34 in³. This is achieved by calculating the volume of one can and multiplying by six.
Explanation:To calculate the total volume of juice in a six-pack where each can is 6 inches tall and has a diameter of 3 inches, we first need to find the volume of one can using the formula for the volume of a cylinder, which is V = πr²h. Since the diameter is 3 inches, the radius (r) is half of that, which is 1.5 inches. Plugging the values into the formula, we get:
Calculate the radius (½ of the diameter): 1.5 inchesCalculate the volume of one can: V = π(1.5 inches)²(6 inches)Find the volume: V = 3.14159 × (1.5 inches)² × 6 inches = × 42.39 in³Multiply by 6 to get the total volume for all six cans: Total volume = 42.39 in³ × 6 = 254.34 in³Therefore, the correct answer is 254.34 in³, which represents the total volume for a six-pack of juice cans.
If m DFC = 40° and m
d = 55°, then mBG=
Answer:
The measure of arc BG is 25°
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
m∠DFC=(1/2)[arc CD+arc BG]
we have
m∠DFC=40°
arc CD=55°
substitute and solve for arc BG
40°=(1/2)[55°+arc BG]
80°=[55°+arc BG]
arc BG=80°-55°=25°
Answer:
The measure of arc BG is 25°
Find the volume of the figure.
Answer:
V = 256 mm3
Hope this helps you out!
Answer:
D,256
Step-by-step explanation:
Use multiplication to do 8*10*3.2 you get 256
How is the volume of a prism calculated?
add the area of the base to the height
subtract the area of the base from the height
multiply the area of the base by the height
divide the area of the base by the height
Multiply the area of the base by the height
Answer:
C) multiply the area of the base by the height
Step-by-step explanation:
Prism is a three dimensional figures.
The volume of a prism calculated by multiplying the area of the base and the height.
Volume of a prism = Base area * height.
For example:
Volume of a rectangular prism = base area * height = (lw)*h = lwh cubic units
Volume of a cube = Base area * height = (a*a)*a = a^2*a = a^3 cubic units
Volume of a cylinder = Base area * height = (πr^2)*h = πr^2 h
The answer is C) multiply the area of the base by the height
If n equals to 37cm and I equals to 12cm what is the length of M?
im not sure of this but I think u have to subtract 37 from 12 and that is 25
I don't know e thats any helpful
What is the length of a diagonal of a cube with a side length of 1 cm?
I know it is 1.73.
But what is the correct answer choice?
A)Square root of 2?
B)Square root of 3?
C)Square root of 4?
D)Square root of 5?
Answer:
The answer is B
Step-by-step explanation:
Answer:
option B. square root of 3
Step-by-step explanation:
In the figure attached the length of one side of the cube is 1 cm.
In the triangle ABC, Side AB = 1 cm
Since side BC is the diagonal of 1 base of the given cube.
Therefore, mBC = [tex]\sqrt{1+1}=\sqrt{2}[/tex] cm
Now we have to calculate the length of diagonal AC.
AC = [tex]\sqrt{AB^{2}+BC^{2}}[/tex]
AC = [tex]\sqrt{1+2}=\sqrt{3}[/tex]
Therefore, option B. square root of 3 will the length of diagonal of the cube.
sally and timothy have two different answers for 1,785 ÷ 35. without dividing, how can you tell whose answer is wrong sally: 1,785 ÷ 35 = 51 timothy: 1,785 ÷ 35= 501
Answer: Timothy's answer is wrong
When you multiply factors, the product with a certain number of place values, the product should have the the sum of the number of place values.
35 has 2 digits.
51 has two digits.
2 + 2 = 4
1785 has 4 digits.
A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute. Approximately how far will a passenger travel during a 5-minute ride? O 132 feet O 659 feet 1,978 feet 3,956 feet
I believe the answer would be 659 feet. Take 42x3= 126 then 126x5 . I get 630 but that’s the closest I got ♀️
The total distance traveled by the Ferris wheel is D = 1,978 feet
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
The circumference of the Ferris wheel can be calculated using the formula:
C = πd
where d is the diameter of the wheel
C = π x 42 feet
C ≈ 131.88 feet
This means that for each rotation of the Ferris wheel, a passenger will travel approximately 131.88 feet
Since the Ferris wheel rotates 3 times per minute, the distance traveled by a passenger in one minute is
131.88 feet/rotation x 3 rotations/minute = 395.64 feet/minute
Therefore, during a 5-minute ride, a passenger will travel approximately
395.64 feet/minute x 5 minutes = 1,978.2 feet
Hence , the total distance is 1,978 feet
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The height of a cylinder is 7 inches. Another cylinder with the same size base has double the volume. What is the height of the second cylinder?
Answer:
since it double the value multiply by 2
Step-by-step explanation:
Answer:
14 inches
Step-by-step explanation:
i got it right
What is 5.193 rounded to the nearest hundredth?
Is it
5.19 is the answer x hope it helped
5.193 rounded to the nearest hundredth is 5.19.
Given is a decimal number 5.193 we need to round to the nearest hundredth,
To round a number to the nearest hundredth, you need to look at the digit in the thousandth place (two decimal places to the right of the decimal point).
In the case of 5.193, the digit in the thousandth place is 3. To round to the nearest hundredth, we follow the following rule:
If the digit in the thousandth place is less than 5, we round down (keep the same value).
If the digit in the thousandth place is 5 or greater, we round up (increase the value by 1).
Since 3 is less than 5, we round down.
Therefore, 5.193 rounded to the nearest hundredth is 5.19.
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The equation for the circle is: x^2 + y^2 + 16x - 24y + 159 = 0
____________________________________________________
Answer:
The center would be (-8,12).
____________________________________________________
Step-by-step explanation:
First,we're going to have to simplify the equation. Here is the work below:
[tex]x^2+y^2+16x-24y+159=0\\\\(x+8)^2-64+y^2-24y+159=0\\\\(x+8)^2+y^2-24y=-159+64\\\\(x+8)^2+(y-12)^2-144=-159+64\\\\(x+8)^2+(y-12)^2=144-159+64\\\\(x+8)^2+(y-12)^2=49\\\\[/tex]
Now, you must use the "form of a circle" equation in order to find out the center and radius of a circle.
The equation is:
[tex](x-h)^2+(y-k)^2=r^2\\\\r=7\\h=-8\\k=12[/tex]
Since we got the answer of:
[tex](x+8)^2+(y-12)^2=49[/tex]
It matches with our equation of [tex](x-h)^2+(y-k)^2=r^2[/tex]
Our "h" represents the x axis on the graph, our "k" represents our y axis on a graph.
Therefore our x value would be -8 and our y value would be 12.
Your FINAL answer should be (-8,12)
____________________________________________________
[tex] {x}^{2} + {y}^{2} + 16x - 24y + 159 = 0 \\ \\ 1. \: x = \frac{ - 16 + 2i \sqrt{(y - 19)(y - 5)} }{2} \: \frac{ - 16 - 2i \sqrt{(y - 19)(y - 5)} }{2} \\ \\ 2. \: x = - 8 + i \sqrt{(y - 19)(y - 5)} \: \: - 8 - i \sqrt{(y - 19)(y - 5)} [/tex]
Make sure you put a comma between them
The ages, in years, of children on the swim team are 10, 11, 12, 12, 11, and 13.
What is the mean age of a child on the swim team?
Answer: 11.5
Step-by-step explanation:
To find the mean first add all the numbers then divide by the amount of numbers you added.
10 + 11 + 12 + 12 + 11 + 13 = 69
69/6 = 11.5
Answer:
[tex]mean=11.5[/tex]
Step-by-step explanation:
By definition the Mean is the average of a set of numbers.
In this case, we know that the ages in years of children on the swim team are the following:
10, 11, 12, 12, 11, and 13
Then, to calculate themean age of a child on the swim team, we need to add up all the numbers and divide this by the total number of values in the set.
You can observe that there are six values. Then, the mean age of a child on the swim team is:
[tex]mean=11.5[/tex]
Plz help ASAP!!!!!! I will give brainliest to the right answer.
How many outcomes do NOT show an even number on the first and show 6 on the second?
Answer:
I believe the answer is 3
Pretty sure it's C.) 5
Hope I helped ¯\_(ツ)_/¯
Solve this system of linear equations. Separate the x- and y- values with a comma. 16x-5y=-28 8x-4y=-8
Answer:
(-3,-4)
Look at attached pictures for work and the text below for the explanation of the work. The brown numbers represent the step number it is.
Step-by-step explanation:
Start by getting either the x or y values in both equations the same number but opposite sign. Ex 16 and -16. I did x. Then add the equations eliminating one variable, in mine it was x, and the solve for the other variable, in mine it was y. Then plug that variable back into one of the two original equations and solve for the other variable, in mine I solved for x.