Answer:
A = 38°
B = 50.32°
C = 91.68°
a = 8
b = 10
c = 12.77
Step-by-step explanation:
The first thing is to find the angle B, like this:
sin B = b * sin A / a = 10 * sin (38 °) / 8
sin B = 0.77
B = arc sin (0.77)
B = 50.32 °
For angle C, it would be:
C = 180 - 38 - 50.32
C = 91.68 °
Side c, we calculate it like this:
c = a * sin C / sin A = 8 * sin (91.68 °) / sin (38 °)
c = 12.77
Rewrite 1/6 with a denominator of 18
Final answer:
To rewrite 1/6 with a denominator of 18, multiply both the numerator and the denominator by 3, resulting in the equivalent fraction 3/18. To confirm its equivalence, simplify 3/18 back to 1/6 by dividing both the numerator and the denominator by 3.
Explanation:
How to Rewrite a Fraction with a New Denominator
To rewrite the fraction 1/6 with a denominator of 18, we need to find a number that we can multiply both the numerator and the denominator of the fraction by so that the denominator becomes 18. Since 6 times 3 equals 18, we will use 3. The fraction then becomes:
(1 x 3) / (6 x 3) equals 3/18.
Verifying the Equivalent Fraction
To verify that 3/18 is indeed equivalent to 1/6, we can simplify 3/18 by dividing both the numerator and denominator by their greatest common factor, which is 3:
3 ÷ 3 / 18 ÷ 3 = 1/6.
This confirms that 3/18 is equal to 1/6 because it simplifies back to the original fraction.
Select all the expressions that have a value
always
greater than 18,204.
A. 18,204 x 6
B. 18,204 x
length
C. 18,204 x 1
use angles
D. 18,204 x
3
10
E. 18,204
Step-by-step explanation:
18024 x 6 = 108144
18024 x 2/3 = 12016
18024 x 1 1/8 = 18025.125
18024 x 3/ 3 = 18024
18024 x 10/5 = 36048
Option A C E are the correct answer
Liz flips a coin 90 times. The coin lands heads up 54 times and tails up 36 times. Complete each statement.
The theoretical probability of the coin landing heads up is
Answer:
1/2 or 50%
Step-by-step explanation:
Please check if that is correct. But generally there are two sides so half of the times it should be heads.
Hope this helps.
The value of Vishal's car is depreciating exponentially.
The relationship between V, the value of his car, in dollars, and t, the elapsed time, in years, since he purchased the car is modeled by the following equation.
V=22,500⋅10^-t/12
How many years after purchase will Vishal's car be worth $10,000
Give an exact answer expressed as a base-10 logarithm.
We have been given that the value of Vishal's car is depreciating exponentially. The relationship between V, the value of his car, in dollars, and t, the elapsed time, in years, since he purchased the car is modeled by the equation [tex]V=22,500\cdot 10^{-\frac{t}{12}}[/tex]. We are asked to find the time, when Vishal's car will be worth $10,000.
To find the time, we will equate our given equation with 10,000 as:
[tex]10,000=22,500\cdot 10^{-\frac{t}{12}}[/tex]
[tex]\frac{10,000}{22,500}=\frac{22,500\cdot 10^{-\frac{t}{12}}}{22,500}[/tex]
[tex]\frac{4}{9}=10^{-\frac{t}{12}}[/tex]
Now we will take log on both sides.
[tex]log_{10}\left(\frac{4}{9}\right)=log_{10}\left(10^{-\frac{t}{12}}\right)[/tex]
[tex]log_{10}\left((\frac{2}{3})^2\right)=-\frac{t}{12}[/tex]
[tex]-\frac{t}{12}=log_{10}\left((\frac{2}{3})^2\right)[/tex]
[tex]-\frac{t}{12}(-12)=(-12)log_{10}\left((\frac{2}{3})^2\right)[/tex]
[tex]t=(-12)log_{10}\left((\frac{2}{3})^2\right)[/tex]
Using property [tex]log(a^b)=b\cdot log(a)[/tex], we will get:
[tex]t=(-12)\cdot 2log_{10}\left(\frac{2}{3}\right)[/tex]
[tex]t=-24log_{10}\left(\frac{2}{3}\right)[/tex]
Therefore, the value of Vishal's car will be $10,000 after approximately [tex]-24log_{10}\left(\frac{2}{3}\right)[/tex] years.
Help to answer this.
Answer: X = 4.5
Step-by-step explanation:
The proportion is 8/9 for the lines. All we have to do is divide 4 by 8/9 to find the exact value of X.
4/(8/9) = 4.5
I hope this helps!
H(t)=t^2+4t+3 what are the zeroes of the function? Write the smaller t first, and then the larger t second
Answer:
t = - 3, t = - 1
Step-by-step explanation:
Given
h(t) = t² + 4t + 3
To find the zeros equate h(t) to zero, that is
t² + 4t + 3 = 0
Consider the factors of the constant term (+ 3) which sum to give the coefficient of the t- term
The factors are + 3 and + 1, since
3 × 1 = 3 and 3 + 1 = 4, thus
t² + 4t + 3 = (t + 3)(t + 1) = 0
Equate each factor to 0 and solve for t
t + 3 = 0 ⇒ t = - 3
t + 1 = 0 ⇒ t = - 1
smaller zero is t = - 3
larger zero is t = - 1
find the value of X
Answer:
[tex]x=\sqrt{13}[/tex] (C.)
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](2^{2} )+(3^{2})=x^{2}[/tex]
[tex]4+9=x^{2}[/tex]
[tex]13=x^{2}[/tex]
[tex]\sqrt{13} =\sqrt{x^{2} }[/tex]
[tex]x=\sqrt{13}[/tex]
Write the Equation of the line that has a slope of -2 and passes through the points (9,5)
Start with the point-slope formula shown at the top in red.
Now, substitute your slope and coordinates in the formula.
Then distribute and combine lie terms.
Finally, add 2x to both sides to get your equation in standard form.
BRAINLIEST!!
1. Solve log2 x = 5.
PLZ HELP
Answer: 32
explanation.
The value of x in the equation log_2_ x = 5 is;
x = 32
We are given; log_2_ x = 5
To solve this, we need to understand that in logarithms, there is a rule for bases like this. An example is;
Log_a_x = y means that;
a^(y) = x
Apply that formula to our question gives us;
log_2_ x = 5 can be expressed as;
2^(5) = x
Thus; x = 32
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The slope-intercept form of the equation of a line that passes through the point (4, -3) is y=-3x+5. What is the point-slope form of the
equation for this line?
Point-Slope Form:y- y1=m(x-x1)
y-3--1/3x+4)
y-4--1/3 (X - 3)
y-4--1/3(x+3)
y+ 3 = -1/3 (x-4)
Answer:
y+ 3 = -1/3 (x-4)
Step-by-step explanation:
Simply plug in the values using (4, -3)
4 = x₁
-3 = y₁
Now one rule to keep in mind when plugging it in, since a negative and a negative make a positive, you have to add three instead of subtracting it.
Answer:
I think the answer is y+ 3 = -1/3 (x-4)
Step-by-step explanation:
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.
Which equation gives the volume of the sphere?
V = two-thirds (27 pi)
V = four-thirds (27)
V = two-thirds (27)
V = four-third (27 pi)
Answer:
C. V = two-thirds (27)
Step-by-step explanation:
Given
Solid Shapes: Cylinder and Sphere
Volume of Cylinder = 27π ft³
Required
Volume of the sphere.
From the question,
We have that
1. The volume of the sphere is the same as the volume of the cylinder
2. The height of the sphere is the same as the height of the cylinder.
From (2) above;
This means that the height of the cylinder equals the diameter of the sphere.
Let h represent the height of the sphere and d represent the diameter of sphere.
Mathematical, d = h
Recall that radius, r = [tex]r = \frac{d}{2}[/tex]
Substitute h for d in the above expression
[tex]r = \frac{h}{2}[/tex]. ----- (take note of this)
Calculating the volume of a cylinder.
V = πr²h
Recall that V = 27; This gives us
27 = πr²h
Divide both sides by h
[tex]\pi r^2 = \frac{27}{h}[/tex]
-------------------
Calculating the volume of a sphere
[tex]V = \frac{4}{3}\pi r^3[/tex]
Expand the above expression
[tex]V = \frac{4}{3}\pi r^2 * r[/tex]
Substitute [tex]\pi r^2 = \frac{27}{h}[/tex]
[tex]V = \frac{4}{3} * \frac{27}{h} * r[/tex]
Recall that [tex]r = \frac{h}{2}[/tex]
So,
[tex]V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}[/tex]
[tex]V = \frac{4}{3} * \frac{27}{2}[/tex]
[tex]V = \frac{2}{3} * 27[/tex]
[tex]V = \frac{2}{3} (27)[/tex]
V = two-third (27)
which polyhedron is represented by the net shown
Answer:
triangular pyramid
Step-by-step explanation:
Let's make the central triangle the "base", or the bottom face, of our polyhedron. Try to visualise what will happen if we fold up the three triangles so that their top vertices meet at the center top (see diagram).
If we can do that, we'll see that it's a pyramid with a triangular base, so it's a triangular pyramid.
What is -22.2 x (-6.1)? A. -135.42 B. -28.3 C. 28.3 D. 135.42
Answer:
D
Step-by-step explanation:
All you have to do is multiply -22.2 by -6.1
Answer: The answer is D
Step-by-step explanation:
John had 60 video games and he sold 80% of the games at a garage sale. How many video games
were sold?
Answer:
48 video games were sold.
Step-by-step explanation:
We know that both 100% and 60 are divisable by 5. 100%÷5=20%. 60÷5=12. So now we know that 20% of 60 is 12. We need 80%, however. To get from 20% to 80%, we just multiply by four. 20 × 4 = 80. But what we do to one side, we must do to the other. 12×4=48. So 80% of 60 is 48.
Hope this helped, and good luck with future math problems!
A hat contains four balls. The balls are numbered 2, 4, 4, and 5. One ball is randomly selected
and not replaced, and then a second ball is selected. The numbers on the two balls are added
together.
A fair decision is to be made about which of three sizes of ice cream cone will be ordered, using
the sum of the numbers on the balls. The sizes are small, medium and large.
Which description accurately explains how a fair decision can be made in this situation?
If the sum is 6 or 7 small cone will be ordered. If the sum is 8medium cone will be ordered. If the sum is 9, a large cone will be ordered
If the sum is 6 or 9. a small cone will be ordered If the sum is 7 a medium cone will be ordered If the sum is 8 large cone will be ordered
the sum is 6, a small cone will be ordered . the sum is 7 or 8 , a medium cone will be ordered. If the sum is 9, a large cone will be ordered.
If the sum is 6, a small cone will be ordered . If the sum is 7 or 9, a medium cone will be ordered If the sum is 8 a large cone will be ordered
Answer: the sum is 6, a small cone will be ordered . the sum is 7 or 8 , a medium cone will be ordered. If the sum is 9, a large cone will be ordered.
Step-by-step explanation:
Based on the question above,
P(6) = P(7 or 8) = P(9)
Hence,
The fair decision can be made if:
the sum is 6, a small cone will be ordered, when the sum is 7 or 8 a medium cone will be ordered and when the sum is 9, a large cone will be ordered.
Please help me out! I have only 1 hour left! I will give brainlist to correct answers. 5 stars and thanks for ALL answers, even asking for details.
Answer:
The small tire would make about 127 rotations.
The large tire would make about 38 rotations.
b. Would you rather ride a bicycle made with two large wheels or two small wheels? Explain.
Two large wheels. Because the larger wheel makes a smoother ride and you spend less energy in order to move, compared to smaller wheels. Also, the larger the diameter, the further it can travel over one revolution.
A bicycle with would allow you to travel farther with each rotation of the pedal.
The larger one. Because in one rotation the larger wheel moves 188.49 inches and the smaller one 56.55 inches.
[tex]C= 188.49\text{inches}[/tex]
[tex]C= 56.55\text{inches}[/tex]
Step-by-step explanation:
- Big wheel 60 inches
- Small wheel 18 inches.
a. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.
Considering: [tex]C=\pi d[/tex]
Large tire:
[tex]C=60\pi[/tex]
[tex]C= 188.49\text{inches}[/tex]
[tex]$C=\frac{188.49}{12} = 15.7 \text{feet}$[/tex]
[tex]$\frac{600 }{15.7} = 38 \text{rotations}$[/tex]
Small tire:
[tex]C=18\pi[/tex]
[tex]C= 56.55\text{inches}[/tex]
[tex]$C=\frac{56.55}{12} = 4.71 \text{feet}$[/tex]
[tex]$\frac{600 }{4.71} = 127 \text{rotations}$[/tex]
What is the x and the y
-5x - 3y = 14
Answer:
[tex]x=-\frac{14+2y}{5}[/tex]
Step-by-step explanation:
That is what i got and i also checked it on a website. so i hope it helps
Consider the parallelogram shown below whose area is 40 square centimeters and height is 8 centimeters. The missing base in the figure is ___ centimeter.
Answer:
5
Step-by-step explanation:
B=a/h
The missing base in the figure is 5 centimeter.
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure. Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.
The area of a parallelogram = Base x Height
Given;
Area of parallelogram= 40 square centimeters
Height of parallelogram= 8cm
Solution;
A= b x h
substituting the given values in the formula;
40= b x 8
b= 40/8
b= 5
So, the answer is 5cm
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PLEASE ANSWER FAST! What does it mean when the point on the number line is an open circle?
Answer:
See explanation for answer.
Step-by-step explanation:
When the point on the number line is an open circle, that means that the inequality does not include that exact value. For instance, in this case the inequality only takes number higher than, but not equal to, -1. Hope this helps!
Answer:
When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".
Step-by-step explanation:
Please Help! I'm really stuck on this question 6th Grade Math
Answer: a
Step-by-step explanation: can i have brainliest
Answer:
155
Step-by-step explanation:
9 x 4 = 36
6 x 9 = 54
5 x 9 = 45
triangles = 10 x 2 = 20
36 + 54 + 45 + 20 = 155
Olivia ordered a shirt online that cost her $38 total.
The package arrived late so the seller took 16% off
the price. How much did she end up paying?
I NEED UT TODAY
Answer:
$6.08
Step-by-step explanation:
38 x 0.16
equals $6.08
Answer:
$31.92
Step-by-step explanation:
Find 16 percent of 38
38*.16= 6.08
subtract
38-6.08= 31.92
Help Me Find The X Please
Answer:
x = 16
y = 16 sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/hyp
sin 60 = y/ 32
Multiply each side by 32
32 sin 60 = y
32 ( sqrt(3) /2) = y
16 sqrt(2)
cos theta = adj/ hyp
cos 60 = x /32
32 cos 60 = x
32 (1/2) =x
16 =x
Answer:
16
Step-by-step explanation:
YOU NEED A CALCULATOR TO SOLVE THIS!
To solve this you need to use SOH-CAH-TOA
Do cos60° to find x
[tex]cos60 = \frac{x}{32}[/tex]
Multiply both sides by 32 to get x alone
[tex]32(cos60) = x[/tex]
Now put 32(cos60) into your calculator
The answer you get is 16
Solve the equation:3/4 (x + 1) = 1/2(x+2)
X=
. (4 + 5) +2 =4+(5+4) true or false
Answer:
False
Step-by-step explanation:
the sum of 198 and h as an algebraic expression
Answer:
198+h
have a nice day
What is the value of f^{-1)(6)
Start at 6 on the y axis. Draw an arrow so that it horizontally moves to the blue curve. Then draw an arrow straight down to vertically drop to x = 4
See the diagram below.
Follow this process in reverse to see that x = 4 leads straight up to the blue curve, and then to the left to land on y = 6. Keep in mind that the inverse reverses the input and output process, which is why I started with y instead of x.
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression, f⁻¹(6) is 4.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the expression can be found as shown below,
y = f(x)
When the value of y is 4, the value of x is 6, therefore, we can write f(6)=4.
Now, the given expression can be simplified as,
f⁻¹(6) = 1 / f(6)
= 1 / 4
= 0.25
Hence, the value of the expression, f⁻¹(6) is 4.
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Two spheres have volumes of 8
area of the larger sphere?
cm
and 64 cm. If the surface area of the smaller sphere is 1671 cm? what is the surface area of the larger sphere?
64cm?
96 cm
128 cm
256cm
The surface area of the larger sphere is 366.2496 square centimeter.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, two spheres have volumes of 87 cm³ and 647 cm³.
We know that, the volume of a sphere = 4/3 πr³
Here, 647 cm³=4/3 πr³
647 = 88/21 r³
r³ = (647×21)/88
r³ = 154.39
r = 5.4 cm
We know that, surface area of a sphere is 4πr².
The surface area of the larger sphere = 4×3.14×5.4²
= 366.2496
Therefore, the surface area of the larger sphere is 366.2496 square centimeter.
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"Your question is incomplete, probably the complete question/missing part is:"
Two spheres have volumes of 87 cm³ and 647 cm³. If the surface area of the smaller sphere is 167 cm², what is the surface area of the larger sphere?
64 cm²
96 cm²
128 cm²
256 cm²
. Which three-dimensional figure is modeled by the net below?
F. rectangular prism
G. triangular prism
H. square pyramid
I. rectangular pyramid
Answer:
Can I get more details on this question?
Step-by-step explanation:
If so, I can probably help you a little bit more. And I will edit my response
Answer: The answer is square pyramid
Step-by-step explanation:
A population has μ = 90 and a standard deviation of σ = 9.6. What are the mean and standard deviation of the sampling distribution x-bar if a sample of 144 were taken?
Answer:
[tex] \mu_{\bar X} = 90[/tex]
[tex] \sigma_{\bar X} =\frac{\sigma}{\sqrt{n}}= \frac{9.6}{\sqrt{144}}= 0.8[/tex]
Step-by-step explanation:
For this case we have a population with the following parameters:
[tex]\mu = 90, \sigma =9.6[/tex]
For this case we have a sample of n= 144 and this sample size is larger (>30) then we can apply the central limit theorem and the distirbution for the sample mean is given by:
[tex] \bar X \sim N( \mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And replacing we got:
[tex] \mu_{\bar X} = 90[/tex]
And the standard deviation is given by:
[tex] \sigma_{\bar X} =\frac{\sigma}{\sqrt{n}}= \frac{9.6}{\sqrt{144}}= 0.8[/tex]
PLEASE HELP ITS AN EMERGENCY
Answer:
the answer is d
Step-by-step explanation: