Answer:
There is a 15% chance a student chosen at random would have brown sandals.
Step-by-step explanation:
The required probability will be 0.15 that a student chosen at random would have brown sandals.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
the probability = number of favorable outcomes / total number of outcomes.
We have been given that out of 200 students in a school, 30 have brown sandals.
To determine the probability that a student chosen at random would have brown sandals.
The probability = number of favorable outcomes / total number of outcomes.
The probability = 30 / 200
The probability = 0.15
Thus, the required probability will be 0.15 that a student chosen at random would have brown sandals.
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If line ab is tangent to circle c , find AC?
Can anyone help?
Answer:
Step-by-step explanation:
If AB is tangent to the circle, the AB makes a right angle with the radius BC. That means that triangle ABC is a right triangle and we need Pythagorean's Theorem to find the missing side which is the hypotenuse.
[tex]AC^2=AB^2+BC^2[/tex] and filling in:
[tex]AC^2=14^2+9^2[/tex] and
[tex]AC^2=196+81[/tex] and
[tex]AC^2=277[/tex] so
[tex]AC=\sqrt{277}[/tex] ≈ 16.64
AC = 16.64
The Tangent theorem
"It states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency."
From given diagram,
tangent AB = 14 units
radius BC = 9 units
Using tangent theorem,
AB is perpendicular to BC.
This means ΔABC is right triangle with ∠B = 90°
Using Pythagoras theorem,
[tex]AC^2=AB^2+BC^2[/tex]
⇒ [tex]AC^2=14^{2}+9^{2}[/tex]
⇒ [tex]AC^2=196+81[/tex]
⇒ [tex]AC^2=277[/tex]
⇒ [tex]AC=\sqrt{277}[/tex]
⇒ [tex]AC=16.64[/tex]
Therefore, AC = 16.64
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if a 30 foot wire is attached to the top of a 12 foot pole and stretched to the ground, find the angle the wire makes with the ground
Answer:
52 degrees
Step-by-step explanation:
Answer:
52 degrees sorry if that's wrong
4x=3y+23
4y+3x=-19
solve by substitution. No files pls
Answer:
x = ⁷/₅
y = ⁻²⁹/₅
Step-by-step explanation:
4x = 3y + 23 (×3)
12x = 9y + 69
4y + 3x = -19
3x = -4y - 19 (×4)
12x = -16y - 76
∴ 9y + 69 = -16y - 76
25y = -145
y = ⁻²⁹/₅
12x = 9(⁻²⁹/₅) + 69
12x = 69 - ²⁶¹/₅
12x = ⁸⁴/₅
x = ⁷/₅
Refer to pictures above real help please
Answer:
38.7°
Step-by-step explanation:
∆ = Tan-1(opposite/ Adjacent)
=Tan-1(8/10)
= 38.66°
= 38.7° to n nearest tenth
A tire has a radius of 20 inches. What is the Circumference of the tire?
Answer:
Step-by-step explanation:
circumference=2πr
=2*3.14*20
=125.6 inches
The circumference of the tire is 125.6 inches.
We have given that,
A tire has a radius of 20 inches.
We have to determine the circumference of the circle
What is the formula for the circumference of the circle?
C=2πr
C=circumference
r=radius of the circle
Use this value in the circumference of the circle
Therefore we get,
=2*3.14*20
=125.6 inches
Therefore the circumference of the tire is 125.6 inches.
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You burn a log on a fire. You use the fire to warm yourself and to light up the
room to read a book. Which energy transformation is taking place?
O A. Thermal energy is transformed to light energy and chemical
energy
B. Chemical energy is transformed to nuclear energy and thermal
energy
C. Nuclear energy is transformed to potential energy and thermal
energy.
D. Chemical energy is transformed to light energy and thermal
energy.
: D. Chemical energy is transformed to light and thermal energy
A vehicle was purchased for $64,000 when exponential depreciation is appeals at the rate of 18% per year, how much will the vehicle be worth 54 month after the purchased date?
Answer:
Step-by-step explanation:
The standard form of an exponential function is
[tex]y=a(b)^x[/tex] where y is the value of the car after x years have gone by, a is the initial value of the car and b is the rate of depreciation. For us, that looks like this:
[tex]y=64000(.18)^{4.5[/tex] where 64000 is the initial value of the car, .18 is the depreciation rate, and 4.5 is 54 months in years. Doing the math on that gives us that the value of the car will be $51,840 4.5 years after it's purchased new.
HELP PLEASE
Find 33/4 x 21/3. All answers must be in lowest terms
[tex] \frac{231}{4} [/tex] ✅
Step-by-step explanation:
[tex] \frac{33}{4} \times \frac{21}{3} \\ = \frac{11 \times 21}{4} \\ = \frac{231}{4} [/tex]
Note:-
A fraction is said to be written in its lowest form if its numerator and denominator are prime, that is, they have no common factors other than 1.[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Find the value of y
Answer:
64-degree ( Alternate angles)
Answer:
y = 64 degree
Step-by-step explanation:
angle y = 64 degree (being alternate interior angles)
y° = 64°
three dimensions
A Pentagon has
A. zero measurements
b. two measurement's
c. three measurements
d. one measurements
Answer:
one measurement
Step-by-step explanation:
hope it's helpful for you ☺️
When the square of a number is increased by 24, the result is eleven times the original. Number find the number
Answer:
the number can be either 8 or 3.
Step-by-step explanation:
Let's define N as the "number"
We know that when the square of this number is increased by 24:
N^2 + 24
we got eleven times the original number, then:
N^2 + 24 = 11*N
We just need to solve this for N
To do it, we first move all the terms to one side of the equation:
N^2 - 11*N + 24 = 0
Now we can use the Bhaskara's formula for the zeros of a quadratic equation:
for a general quadratic equation:
a*x^2 + b*x + c = 0
the roots or zeros are given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
We get then:
[tex]N = \frac{-(-11) \pm \sqrt{(-11)^2 - 4*1*24} }{2*1} = \frac{11 \pm 5}{2}[/tex]
So we have two solutions:
N = (11 + 5)/2 = 16/2 = 8
N = (11 - 5)/2 = 6/2 = 3
So the number can be either 8 or 3.
squareroot of
[tex]12 \frac14[/tex]
Answer:
7/2
Step-by-step explanation:
12 1/4 is equivalent to the improper fraction 49/4.
The square root of 49/4 is 7/2.
The squareroot of [tex]12 \frac14[/tex] is [tex]3 \frac{1}{2} [/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{12 \frac{1}{4} } \\ \\ = \sqrt{ \frac{49}{4} } \\ \\ = \sqrt{ \frac{7 \times 7}{2 \times 2} } \\ \\ = \sqrt{ \frac{( {7})^{2} }{( {2})^{2} } } \\ \\= \frac{7}{2} \\ \\ = 3 \frac{1}{2} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Someone please help it’s the last question of my final.
Answer: $46,619
»» 288.44 / 0.7%
»› 41,205
»» 45 x 120.33
»» 5,414
A=41,205
A=5,414
A=46,619
[tex]\color{yellow}{}[/tex]
Answer:
The answer would be $46,619
Step-by-step explanation:
Someone already explained it pretty well, goodluck! :)
How can you apply the concept of area and perimeter in your everyday life?
2x + (-x) + 5 + (-5) =
Answer:
X
Step-by-step explanation:
2x-x=x
5-5=0
Answer:
[tex]2x + (-x) + 5 + (-5) = x[/tex]
Step-by-step explanation :
Remove Parenthesis :
[tex]2x - x + 5 - 5[/tex]
Add similar elements :
[tex]x + 5 - 5[/tex]
Add them up :
[tex]5 - 5 - 0 = x[/tex]
Plz help what is the perimeter of the rectangle
Answer:
18 units
Step-by-step explanation:
The base is 7-4 = 3 units
The height is 8 - 2 = 6 units
P = 2(b+h)
P = 2( 3+6)
P = 2(9)
P = 18
Which is the rationalized form of the expression. A, B , C, or D?
Answer:
C
Step-by-step explanation:
Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.
You get answer C.
Your score on a game show is -150. You answer the final question correctly, so you get 400 points. what is your final score?
Answer:
250
Step-by-step explanation:
-150 + 400 = 250
Final Score= -150 + 400
= 250 --- (Answer)
The book wants me to use the Pythagorean Theorem (a^2+b^2=c^2) to get the correct answer. I never learned how to use the theorem when finding distance and have only used Distance Formula. I tried using the Distance Formula to get the correct answer and got a negative outcome. Can someone please explain how Pythagorean Theorem works or maybe tell me how to fix the Distance Formula so it doesn't give me a negative outcome.
Answer:
C) [tex]\sqrt{106}[/tex] units
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are side lengths of a right triangle and [tex]c[/tex] is the hypotenuse, the longest side of the right triangle.
The distance formula is similar to that of the Pythagorean Theorem which is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points that you wish to find the distance between them in an (x,y) coordinate plane.
Here, we are given that [tex](x_1,y_1)[/tex] is [tex]P(-4,-6)[/tex] and [tex](x_2,y_2)[/tex] is [tex]Q(1,3)[/tex]. So, we can use the distance formula as described previously to find the positive distance between the two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(1-(-4))^2+(3-(-6))^2}[/tex]
[tex]d=\sqrt{(1+4)^2+(3+6)^2}[/tex]
[tex]d=\sqrt{(5)^2+(9)^2}[/tex]
[tex]d=\sqrt{25+81}[/tex]
[tex]d=\sqrt{106}[/tex]
[tex]d \approx 10.295630141[/tex]
Since all of the given answer choices are in radical form, then C is the correct answer. The distance between the two points is [tex]\sqrt{106}[/tex] units.
Which is a solution for the following system of inequalities?pls help :3
(0,5)
(0,-2)
(1,-1)
(0,0)
f(x)=(41)x
Exponential growth or Exponential decay
Answer:
growth
Step-by-step explanation:
Hey! can someone help me find the value of x please??!
Answer:
I think it´s 2.
Step-by-step explanation:
7(2) = 14
14+5=19
Pretty simple math for me, not sure about you though.
Answer:
x=2
Step-by-step explanation:
since the two angles are equivalent to each other, we also know that the legs of triangle are equal... so we set the legs equal to each other and solve for x...
7x+5=19
subtract five from both sides
7x=14
divide 7 from both sides
x=2
Solve the following equation for x: 2x^2 - 3 = 47
With explanation plz ion wanna go summer school
Answer:
Step-by-step explanation:
2x²-3=47
2x²=47+3
x²=50/2=25
x=±√25=±5
Answer:
x = ±5
Step-by-step explanation:
2x^2 - 3 = 47
Add 3 to each side
2x^2 - 3+3 = 47+3
2x^2 = 50
Divide each side by 2
2x^2 = 50/2
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = ±5
answer please need belp ???
What does the transformation f(x) --> -f(x) do to the graph of f(x)
Answer: D) Reflect over x-axis
=======================================================
Explanation:
When we do this type of reflection, a point like (1,2) moves to (1,-2).
As another example, something like (5,-7) moves to (5,7)
The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.
We can say that [tex](x,y) \to (x,-y)[/tex] as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.
If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.
There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.
Charles is cooking enough lentils for lentil barley soup and lentil salad. The soup recipe calls for 3/4 cup of dried lentils. The salad recipe calls for 1 1/ 2 cups of dried lentils. Jon has a 1/8 -cup scoop. How many scoops of dried lentils will Charles need to have enough for the soup and the salad?
Answer:
18 scoops is the correct answer
Step-by-step explanation:
3/4 can also be written as 6/8 (multiply both 3 and 4 by 2)
and 1 1/2 is actually 3/2 which can be written as 12/8 (multiply both 3 and 2 by 4)
thus total lentils required is 6/8 + 12/8 = 18/8 cups.
with scoop size 1/8 cup you'll need 18 scoops .
Answer:
18 1/8 scoops
Step-by-step explanation:
Soup:
6 scoops from a 1/8 cup can make a 3/4 cup
Salad:
4 scoops from a 1/8 cup can make a 1/2 cup
If 1/8 means one portion is divided into eight portions, then 8 scoops from a 1/8 cup can make 1 cup.
A clothing store purchases T-shirts for
$4.00 each and then marks up the price
of each by 55%. What is the markup and
new price of each T-shirt?
Answer:
The mark up is $2.20 and the new price of each T-shirt is $6.20.
Step-by-step explanation:
Before we find the new price of each T-shirt we must find the markup (by how much were raising the price).
The problem states each T-shirt costs $4.00, but then marks up the price of each by 55%.
Step 1 would be to find 55% of $4.00.
0.55 * 4 = 2.2
So that is the mark up, the price is going up by $2.20. To find the new price of each T-shirt, you take that $2.20 and add it to the original $4.00.
$4.00 + $2.20 = $6.20
So the mark up is $2.20 and the new price of each T-shirt is $6.20.
If c+di is a point on the circle, then
|c + dil=
cosy/1-siny = 1+siny/cosy
varify using trig identity.
Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:
[tex]\displaystyle \frac{\cos y}{1-\sin y}=\frac{1+\sin y}{\cos y}[/tex]
On the left, we can multiply both layers by (1 + sin(y)):
[tex]\displaystyle \frac{\cos y}{1-\sin y}\left(\frac{1+\sin y}{1+\sin y}\right)=\frac{1+\sin y}{\cos y}[/tex]
Multiply:
[tex]\displaystyle \frac{\cos y(1+\sin y)}{1-\sin^2 y}=\frac{1+\sin y}{\cos y}[/tex]
From the Pythagorean Theorem, we know that sin²(y) + cos²(y) = 1. Hence, 1 - sin²(y) = cos²(y). Substitute:
[tex]\displaystyle \frac{\cos y(1+\sin y))}{\cos^2 y}=\frac{1+\sin y}{\cos y}[/tex]
Cancel:
[tex]\displaystyle \frac{1+\sin y}{\cos y}=\frac{1+\sin y}{\cos y}[/tex]
Hence proven.
Solve the expression for a=12 , b=6 and c=3
Answer:
50
Step-by-step explanation:
Substitute.
Answer:
320
Step-by-step explanation:
(6 x 3)² - 2(12) ÷ 6
324 - 24 ÷ 6
324 - 4
= 320