Answer:
y = -6x - 200
Step-by-step explanation:
1.What values could replace the "?" in these equations to make them true?
2. How would you explain to a friend who doesn't know about logarithms what the equation
LaTeX: \log_{10}x\:=\:y
log
10
x
=
y
says about x and y?
Answer:
Remember that logarithms are inverse of exponentials. That means the result of the logarithm is equal to the exponent of a power with the same base.
1. (a)[tex]log_{10} (10)=1[/tex]
Notice that the result is one beacuse [tex]10^{1}=10[/tex]
(b)[tex]log_{10}(10000)=4[/tex]
Because [tex]10^{4}=10000[/tex]
(c)[tex]log_{10}(?) =7 \implies 10^{7} =10000000[/tex]
So, [tex]log_{10}(10000000)=7[/tex]
2.I would say to thim that [tex]x[/tex] and [tex]y[/tex] are variables of the logarithm, which be solved by imagine the logarithm as an exponential like
[tex]log_{10} (x)=y \implies 10^{y}=x[/tex]
In other words, the [tex]y[/tex] is the exponent and the [tex]x[/tex] is the result of the exponential.
Carl pays $45 per month for car insurance. How much does he spend on car insurance in 1 year?
Answer:
He spends $540
Step-by-step explanation:
literally just 45 multiplied by 12
help Marshmello ok xd
Answer:
84
Step-by-step explanation:
We simply plug in 1.75 for x into y = 48x, and when we do so we get y = 48 * 1.75 = 84 cups of coffee. Hope this helps!
Answer:
B) 84
Step-by-step explanation:
48 times x is the cups of coffee sold in x hours.
if x = 1.75, then you times 48 by 1.75
48 x 1.75 = 84
calculo la superficie de las figuras sabiendo que cada cuadrado mide 5m2
individual health insurance is usually less expensive than group health insurance
true or false?
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Sin2x + cos3x expand the expression
Step-by-step explanation:
Use double and triple angle identities:
sin(2x) + cos(3x)
2 sin x cos x + 4 cos³x − 3 cos x
What is a tangent line in relation to a circle?
Answer:
A tangent to a circle is a straight line which touches the circle at only one point.
Step-by-step explanation:
This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.
Circle B is shown. Line segments C B, D B, and E B are radii. Angle C B E is 52 degrees and angle E B D is 160 degrees. What is the measure of Arc C E D? 106° 108° 148° 212°
Answer it would be 212 :)
Step-by-step explanation:
The measure of arc CED in the circle given is: D. 212°.
What is the Measure of an Arc of a Circle?Measurement of an arc of a circle = measure of its central angle.
Thus:
Measure of arc CED = angle CBE + angle EBD
Substitute
Measure of arc CED = 52 + 160
Measure of arc CED = 212°
Therefore, the measure of arc CED in the circle given is: D. 212°.
Learn more about measure of arc on:
https://brainly.com/question/1239071
The ratio of the number of boys to the number of girls in a class is 12:13 What percentage of the class are boys?
48%
Step-by-step explanation:
add the ratio together which is 25
pick the ratio of boy
divide 12 by 25 and multiply 100
12/25×100= 48%
Answer:
48%
Step-by-step explanation:
b/g=12/13
so b/12=g/13=k
b=12k
g=13k
so b+g=25k so k=b+g/25
b=12*(b+g)/25=12*4*(b+g)/25*4=48(b+g)/100
so 48% are boys
One hundred examiners each marking eighty scripts per day are needed to mark an examination in fourteen days.How many days would two hundred examiners each marking forty scripts per day take to mark the same examination?
Answer:
SOS
Step-by-step explanation:
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What is the circumference of a circle with a radius of 91 mm? (use 22/7 for pi; show your work in numbers)
Answer:
[tex] \boxed{Circumference \: of \: circle = 572 \: mm} [/tex]
Step-by-step explanation:
Radius (r) = 91 mm
[tex]Circumference \: of \: circle = 2\pi r \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \frac{22}{7} \times 91 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 22 \times 13 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 44 \times 13\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 572 \: mm[/tex]
According to the picture, whats the answer?
Answer:
84 meters
Step-by-step explanation:
5 x 6 = 30 hypotenuse side not shown
3 x 4 ÷ 2 x 2 = 12 red (both ends)
3 x 6 = 18 green side
6 x 4 = 24 blue side
The string of a kite is 100 meters long and it makes an angle of 60° with the ground. What is the height of the kite?
Show your work please)
Answer:
50√3 ≈ 86.6 m
Step-by-step explanation:
The geometry can be modeled by a right triangle with the height of the kite being the leg opposite the 60° angle. The hypotenuse has the given length of 100 m.
The mnemonic SOH CAH TOA reminds you that the relation between angles and the sides of interest here is ...
Sin = Opposite/Hypotenuse
sin(60°) = (kite height)/(100 m)
kite height = (100 m)·sin(60°) = (100 m)(√3)/2
kite height = 50√3 m ≈ 86.6 m
A flat object with two sides, one colored red (R), the other green (G), is tossed 2 times. List all possible outcomes of the experiment.
Answer:
3 possible outcomes
Step-by-step explanation
1) R R
2) R G
3) G G
2 sin^2 + sin x - 3 = 0
Answer:
x = 2 π n_1 + π/2 for n_1 element Z
or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z
Step-by-step explanation:
Solve for x:
-3 + sin(x) + 2 sin^2(x) = 0
The left hand side factors into a product with two terms:
(sin(x) - 1) (2 sin(x) + 3) = 0
Split into two equations:
sin(x) - 1 = 0 or 2 sin(x) + 3 = 0
Add 1 to both sides:
sin(x) = 1 or 2 sin(x) + 3 = 0
Take the inverse sine of both sides:
x = 2 π n_1 + π/2 for n_1 element Z
or 2 sin(x) + 3 = 0
Subtract 3 from both sides:
x = 2 π n_1 + π/2 for n_1 element Z
or 2 sin(x) = -3
Divide both sides by 2:
x = 2 π n_1 + π/2 for n_1 element Z
or sin(x) = -3/2
Take the inverse sine of both sides:
Answer: x = 2 π n_1 + π/2 for n_1 element Z
or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z
what does the pythagorean theorem and it’s Converse state? why is this theorem important? what are some real world examples in which this theorem is used?
Answer:
The converse of the Pythagorean Theorem states that: If the square of the longest side of the triangle is equal to the sum of the squares of the other two sides of the triangle, then the triangle is a right triangle.
Step-by-step explanation:
Determine the slope of the line that passes through the points: x−8,0,4,5,y,−33,−1,15,19
Answer:
The equation of a line y = ax + b passes point (-8, -33) and point (0, -1) can be formulated by:
(Note: we do not need all of 4 points, 2 points are enough)
-33 = a x (-8) + b
-1 = a x 0 + b
From 2nd equation, we have:
b = -1
From 1st equation, we have:
b - 8 x a = -33
=> -1 - 8 x a = -33
=> 8 x a = 32
=> a = 4
=> The equation of line: y = 4a - 1
Hope this helps!
:)
FOR BRAINLIEST only RIGHT ANWERS
Answer:
Length of arc: 6π
Step-by-step explanation:
~ Let us answer this question in terms of π, remaining so ~
1. Assume that this is a complete circle, for the moment being. The chord with length of 12 units would act as the diameter, and using that information we could determine the circumference of this complete circle...which will help us in the future. Apply the formula π * d as such: π * 12 ⇒ 12π to get the circumference as 12π.
2. Knowing that the length of the complete circle's circumference is 12π, this arc is part of a semicircle, meaning that it's value would be half of that of the complete circle's circumference, or in other words: 12π/2 ⇒ Answer ~ Length of arc: 6π
Answer:Length of arc: 6π
Step-by-step explanation:
What is the quotient?
(6 * 108) = (1.5 * 10-4)
4 x 1012
4 x 104
4 x 10-32
410-2
Answer:
(A)[tex]4X10^{12}[/tex]
Step-by-step explanation:
Given the quotient:
[tex]\dfrac{6*10^8}{1.5*10^{-4}}[/tex]
To evaluate, we first separate the given expression as follows.
[tex]=\dfrac{6}{1.5}X\dfrac{10^8}{10^{-4}}[/tex]
Next, we apply the division law of indices to the powers of 10.
Division Law of Indices: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]=4X10^{8-(-4)}\\=4X10^{8+4}\\=4X10^{12}[/tex]
Therefore, our quotient is [tex]4X10^{12}[/tex].
The correct answer is A.
Find x when
-1/2
+
X
=
-21/4
Answer:
-19/4
Step-by-step explanation:
-1/2 + x =-21/4
x=-21/4+1/2
x=-21/4+2/4
x=-19/4
Which figure has a greater area?
19 ft
16.4 ft
.
15 ft
16.1 ft
Answer:
green triangle
Step-by-step explanation:
The green triangle has an area of
A = 1/2 bh
A = 1/2 (15) * 19
A =142.5 ft^2
The blue triangle has an area of
A = 1/2 bh
A = 1/2(16.1) (16.4)
A =132.02 ft^2
The green triangle has a greater area
A clothing company produces denim jeans. The jeans are made and sold with either a regular cut or a boot-cut. To estimate the proportion of all customers in Tacoma, WA, who prefer boot-cut jeans, a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans. Construct the 99% confidence interval to estimate the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans and interpret the confidence interval (please write the interval boundaries to THREE decimal places
Answer:
99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].
Step-by-step explanation:
We are given that a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans.
Firstly, the Pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of customers who purchased boot-cut jeans = [tex]\frac{56}{178}[/tex] = 0.315
n = sample of customers = 178
p = population proportion of customers who prefer boot-cut jeans
Here for constructing 99% confidence interval we have used One-sample z test for proportions.
So, 99% confidence interval for the population proportion, p is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex], [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.315-2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }[/tex] , [tex]0.315+2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }[/tex] ]
= [0.225 , 0.405]
Therefore, 99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].
The interpretation of the above confidence interval is that we are 99% confident that the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans will lie between 0.225 and 0.405.
What would you do to find the arc length around 5/8 of a circle?
Answer:
5/8 * 2 * pi *r
Step-by-step explanation:
First find the circumference of the circle
C = 2 * pi *r
Then multiply it by the fraction of the circle ( arc length) you wish to find
5/8 * 2 * pi *r
What is the solution to the equation? 5 = two-fifths a 2 4 and three-fifths 12 and one-half 25
Answer:
12 1/2
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of a.
5 = (2/5)a
5(5/2) = (2/5)(5/2)a
25/2 = a
12 1/2 = a . . . . written as a mixed number
The solution is 12 1/2.
Answer:
12 1/2
Step-by-step explanation:
a desert tray has three slices of cake, three key lime pies, and four ice cream sundaes. What is the probability of the next two customers both select key lime pie?
Answer:
The probability of the next two customers both select key lime pie is 1/15
Step-by-step explanation:
No. of slices of cakes = 3
No. of key lime pies = 3
No. of ice cream sundaes = 4
Total deserts = 3+3+4=10
We are supposed to find The probability of the next two customers both select key lime pie
Probability of selecting key lime pie by first customer =[tex]\frac{3}{10}[/tex]
So,Total deserts =10-1=9
No. of key lime pies = 3-1=2
So,Probability of selecting key lime pie by second customer = [tex]\frac{2}{9}[/tex]
So,the probability of the next two customers both select key lime pie=[tex]\frac{3}{10} \times \frac{2}{9} =\frac{1}{15}[/tex]
Hence the probability of the next two customers both select key lime pie is 1/15
PLEASE HELP
Sara and Sam are each working on a science project in which they need to research the individual masses of the nine planets (including the dwarf planet Pluto as the ninth planet). Sara completes her data for the planets' masses in kilograms while Sam's data is in milligrams.
Sara:
Approximate how many times greater Saturn's mass is than Mercury's.
A: 2,000,000
B: 200,000
C: 20,000
D: 2,000
Match the expressions to their limit values.
Answer:
Step-by-step explanation:
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
The equation of circle is :
(x−a)² + (y−b)² = r²
So the equation is
(x-3)² + (y-(-2))² = (6)²
Where center = (a,b) = (3,-2) and
Radius = r = 6
Grace swam 0.6 kilometers during her first week of training and 0.25 kilometers during her second week of training. How many kilometers did she swim in all?
A.3.1 kilometers
B.8.5 kilometers
C.0.31 kilometers
D.0.85 kilometers
Answer:
she will cover a distance of 0.85 km.
Step-by-step explanation:
We have,
Grace swam 0.6 kilometres during her first week of training and 0.25 kilometres during her second week of training.
It is required to find total distance covered by her in all.
It can be calculated simply adding the distance covered in first and second week of training. So,
Total distance, D = 0.6 km +0.25 km = 0.85 km
Hence, she will cover a distance of 0.85 km.
An experienced landscaper thought it would be funny to play a joke on some rookie landscapers. The rookies were given the measurements, l e n g t h equals 4 space cube root of 24 f t space a n d space w i d t h equals 6 space cube root of 3 space f t , and asked to find the exact area (no decimals) of the rectangular region they would be working with. Show the equation and all work needed to find the exact area in simplest form. Be sure to write a sentence explaining your answer. Don’t forget the label! Note: we want the exact area, which is not a decimal. Instead, provide the answer in simplest radical form.
Answer:
48∛9 ft²
Step-by-step explanation:
The length (L) and width (W) are given by:
[tex]L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}[/tex]
Since this is a rectangular region, the area is given by:
[tex]A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2[/tex]
The answer can be further simplified by factoring as follows:
[tex]A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2[/tex]
The exact area is its simplest form is 48∛9 ft²