Answer:
sin 47° = 0.731
Step-by-step explanation:
the complementary angle to 43° is 47°
sin 47° = 0.731
Answer:
0.731
Step-by-step explanation:
Because of the identity
cos x = sin(90-x).
Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios.
Which table shows the same data?
Answer:
It would be the second table
Step-by-step explanation:
If you look at the three points on the graph, (2,3) (4,6) (6,9), the should correspond or match with the x and y values in the table.
In the second table, the x values are 2, 4, and 6. the y values are 3, 6, and 9.
Y=x^2+4x+6 find the domain and range
Domain:(−∞,∞),{x|x∈R}
Range:[2,∞),{y|y≥2}
The Domain is {1, 2, 3, 4} and the range is { 11, 18, 27, 38}
What is Domain and Range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given:
Y=x^2+4x+6
As, we know that domain is the input value and range is the output value.
Then, x = 1
y = 1 + 4 +6
y= 11
and, x= 2
Y = 4 + 8 +6
Y = 18
and, x= 3
Y = 9 + 12 + 6
Y = 27
and, x = 4
Y = 16 + 16 + 6
Y = 38
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blank plus 1/2 equals to 4/6
Answer:
The fraction in the blank is 1/6!
Step-by-step explanation:
First:
X + 1/2 = 4/6
-1/2. -1/2
4/6 - 1/2 = 1/6
X = 1/6
So the blank is 1/6
What is the value of log, 81?
2
3
4
5
Answer:
log 81 = 1.90849
Step-by-step explanation:
log 81 = log 9^2 = 2 log 9 = 2(0.95424) = 1.90849
The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 9.4% per hour.
How many hours does it take for the size of the sample to double?
Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
oo
E
Answer:
It takes 7.37 hours for the size of the sample to double.
Step-by-step explanation:
Continuous exponential growth model:
The continuous exponential growth model for populations is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate parameter, as a decimal.
Growth rate parameter of 9.4% per hour.
This means that [tex]r = 0.094[/tex]
So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(t) = P(0)e^{0.094t}[/tex]
How many hours does it take for the size of the sample to double?
This is t for which P(t) = 2P(0). So
[tex]P(t) = P(0)e^{0.094t}[/tex]
[tex]2P(0) = P(0)e^{0.094t}[/tex]
[tex]e^{0.094t} = 2[/tex]
[tex]\ln{e^{0.094t}} = \ln{2}[/tex]
[tex]0.094t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.094}[/tex]
[tex]t = 7.37[/tex]
It takes 7.37 hours for the size of the sample to double.
Find angle x to the nearest tenth.
47
73
78
A) 36.1
B) 66.2
C) 26.3
D) 31.6
The dot plots show the number of hours a lightbulb lasts from two different brands. Brand A. Number of hours per lightbulb 1000 4200 1400 1500 1800 2000 Brand B Number of hours per lightbulb .. 1200 1400 1600 1800 2000 Which of the following statements is correct? A. There were more lightbulbs in the dot plot for brand B than in the dot plot for brand A. B. The mean for brand A is the same as the mean for brand B. C. The mean for brand A is higher than the mean for brand B. D. The mean for brand B is higher than the mean for brand A.
Answer:
Step-by-step explanation:
The mean for brand A is higher than the mean for brand B
The mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have:
For brand A:
The number of hours per lightbulb:
1000, 4200, 1400, 1500, 1800, 2000
Mean for brand A:
[tex]\rm Mean(A) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]
[tex]\rm Mean(A)= \frac{1000+4200+1400+1500+1800+ 2000}{6}[/tex]
[tex]\rm Mean(A)= \frac{11900}{6}\\\\\rm Mean(A) = 1983.33[/tex]
For Brand B:
The number of hours per lightbulb:
1200, 1400, 1600, 1800, 2000
Mean for brand B:
[tex]\rm Mean(B) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]
[tex]\rm Mean(B)= \frac{1200 +1400 +1600 +1800 +2000}{6}[/tex]
[tex]\rm Mean(B)= \frac{8000}{5}\\\\\rm Mean(B) = 1600[/tex]
We can see that:
Mean(A) > Mean(B)
Thus, the mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.
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Find the values of x and y. Write your answers in simplest form.
Answer:
x = 5√2
y = 15
Step-by-step explanation:
By applying sine rule in the given right triangle,
sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{y}{10\sqrt{2}}[/tex]
y = [tex]\frac{\sqrt{3} \times 10\sqrt{2} }{2}[/tex]
y = 15
Similarly, by applying cosine rule in the given triangle,
cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{2}=\frac{x}{10\sqrt{2}}[/tex]
x = 5√2
Simplify and write answer in standard form.
then show work
Answer:
81a²b²
Step-by-step explanation:
(-9ab)² = (-9ab)(-9ab) = 81a²b²
Answer:
[tex]81a^{2} b^{2}[/tex]
Step-by-step explanation:
(-9ab)^2
(-9)^2×a^2b^2
Evaluate the power
81a^2b^2
81a^2b^2
hope it helps...
have a great day!!
If f(x) = 2x^2 + 4x + 7, find f'(-5), using the definition of derivative. f'(-5) is the limit as x → -5
of the expression ?
The value of this limit is ?
Using the limit definition of the derivative, you have
[tex]\displaystyle f'(-5) = \lim_{x\to-5} \frac{f(x) - f(-5)}{x - (-5)} = \lim_{x\to-5} \frac{(2x^2+4x+7) - 37}{x + 5}[/tex]
Simplify the numerator:
(2x ² + 4x + 7) - 37 = 2x ² + 4x - 30
… = 2 (x ² + 2x - 15)
… = 2 (x + 5) (x - 3)
Then
[tex]\displaystyle f'(-5) = \lim_{x\to-5}\frac{2(x+5)(x-3)}{x+5} = \lim_{x\to-5} 2(x-3) = \boxed{-16}[/tex]
• • •
For your second question in the comments, if f(x) = -2x ² + 3x - 7, then by the definition of the derivative, you have
[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{(-2(x+h)^2+3(x+h)-7) - (-2x^2 + 3x - 7)}h[/tex]
Simplify the numerator:
(-2 (x + h)² + 3 (x + h) - 7) - (-2x ² + 3x - 7)
… = (-2x ² - 4xh - 2h ² + 3x + 3h - 7) - (-2x ² + 3x - 7)
… = -4xh - 2h ² + 3h
Now compute the limit:
[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{-4xh-2h^2+3h}h = \lim_{h\to0}(-4x-2h+3) = \boxed{-4x+3}[/tex]
what is the answer to x+2=17-4x
Answer:
x = 3
Step-by-step explanation:
Move all terms containing x to the left
5x + 2 = 17
Move all terms not containing x to the right
5x = 15
Divide each term by 5 and simplify
x = 3
Starting at noon, Emily observed the amount of snow on her lawn during a blizzard.
She wrote an equation to represent s, how many inches of snow were on the lawn:
S = 0.024x + 7, where x represents the number of minutes past noon. What could
the number 0.024 represent in the equation?
Answer:
0.024 represents the amount of snow that is added to the lawn every minute.
Step-by-step explanation:
Emily observed the amount of snow on her lawn during a blizzard. So, 0.024 in the equation shows the rate at which snow is coming with the number of minutes passing.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
For an unknown quantity represented by an unknown variable, equations are then solved to determine its value. It is clear that a statement is not even an equation if there is no "equal to" sign in it.
As per the given equation in the question,
S is the snow in inches.
x shows the time in minutes and,
0.024 is the rate along with the time at which the snow is accumulating in the lawn and 7 in the equation is the constant value.
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Which number is not the mean, median, mode, or range of the data set 4, 3, 15, 11, 3, 8, 7,5?
Answer:
15
Step-by-step explanation:
Answer:
The answer is
Step-by-step explanation:
Mean 7
Median 6
Mode 3
Range 12
Two angles are supplementary. The larger angle is 56° more than the smaller angle. Find the measures of both angles in degrees.
The area of the state of Nevada can be estimated using a trapezoid. Estimate the area of the state of Nevada.
A. 31,672 mi2
B. 78,980 mi2
C. 110,622 mi2
D. 131,327 mi2
Answer: 31,672 mi2
Step-by-step explanation:
The area of the state of Nevada can be estimated using a trapezoid
1⁄2 · n = 3 I don't know what to do
Answer:
n=6
Step-by-step explanation:
[tex]\frac{1}{2} n=3[/tex]
Multiply both sides by 2
2*1/2n=3*2
Simplify;
n=6
Answer: n=6
Step-by-step explanation:
6*1/2=3 so this is y n=6.
Express the ratios as a fraction without reducing.
a. 6 : 13
b. 7 : 40
c. 45 : 36
d. 37 : 43
Answer:
a
Step-by-step explanation:
12345678900987653321
In a fruit cocktail, for every 25 ml of orange juice you need 30 ml of apple juice and 45 ml of coconut milk. What proportion of the cocktail is coconut milk?
Give your answer as a fraction in its simplest form.
Answer:
9/20
Step-by-step explanation:
45/100 or 9/20
Emily and Fred each have some money.
Gary has no money.
Emily gives £9 to Gary.
Fred gives £6 to Gary.
Now they all have the same amount of money.
a) How much money did Emily have to begin with?
£
b) How much money did Fred have to begin with?
£
Answer
Assalam waliakum
Answer:
Step-by-step explanation:
If I add Gary's money
9+ 6 = 15
Emily have to begin with, $ 24
15 + 9 = 24
Fred have to begin with $ 21
15 + 6 =21
I need this ASAP please thank you
Your math teacher tells you that your fish tank will have a capacity of about 976 cups. You have a total of 30 tropical fish. For them to flourish in a fish tank, there needs to be an average of 2 gallons of water for each fish.
Convert 976 cups to gallons.
976 cups equals
gallons.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The tank can not keep 30 tropical fish in it.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Since there needs to be an average of 2 gallons of water for each fish and there are a total of 30 tropical fish. Therefore, the amount of water needed for a total of 30 fish to flourish is,
Amount of water needed = 30 fish × 2 gallons = 60 gallons
Since One gallon is equal to 19.2152 cups. Therefore, the amount of water needed for the fish to flourish is,
60 gallons = 60 × 19.2152 cups = 1152.912 cups
Since the tank has a capacity of 976 cups only, the tank is not big enough to keep 30 fish.
Hence, the tank can not keep 30 tropical fish in it.
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Suppose a jar contains 12 red marbles and 18 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer in decimal form, rounded to the nearest thousandth.
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 99% confidence interval with a maximum error of 0.1 reproductions per hour. Assuming that the mean is 6.1 reproductions and the variance is known to be 5.76, what is the minimum sample size required for the estimate? Round your answer up to the next integer.
Answer:
The minimum sample size required for the estimate is of 3820.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Variance is known to be 5.76
This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]
What is the minimum sample size required for the estimate?
Maximum error of 0.1 means that we find n for which M = 0.1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 2.575\frac{2.4}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 2.575*2.4[/tex]
Multiplying both sides by 10
[tex]\sqrt{n} = 2.575*24[/tex]
[tex](\sqrt{n})^2 = (2.575*24)^2[/tex]
[tex]n = 3819.2[/tex]
Rounding up:
The minimum sample size required for the estimate is of 3820.
Which line is perpendicular to 5y + 2x = 10?
2x + 5y = 10
10x - 4y = 8
y + 5x = -2
y = - 2x + 10
Choose the correct answer below.
O A. y = - 2x + 10
OB. 10x - 4y = 8
O C. y + 5x = -2
OD. 2x + 5y = 10
Which expression is equivalent (With explanation)
Answer:
log_7(6)
Step-by-step explanation:
log_7(2)+log_7(3)
log_7(2×3)
log_7(6)
PLEASE HELP ME I AM GIVING 30 POINTS PLEASEEE
A 21 inch TV costs $150. It is advertised on sale for 32% off. What is the cost savings? Solve using two different methods.
Answer:
$48 in savings
Step-by-step explanation:
1.
150-(150*32%)=102
150-102=48
2.
30% of 150 is 45
2% of 150 is 3
45 plus 3 is 48
Please brainliest! I did both methods and explained!
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the quotient.
=
Answer:
7
Step-by-step explanation:
2+2+3
can someone help me answer these short questions? thank you!
Answer:
#1 - a mathematical relationship or rule expressed in symbols which help you solve something
#2 - variables, which represent an aspect of the problem
#3 P is perimeter, L is length, W is width, A is area
#4 Because in order to find the perimeter, you need to multiply the length and the width twice then add them.
Step-by-step explanation:
PLEASE ANWER FAST!!!!! 100 x 6302= THANKS!!!!!!!!!!
Answer:
630,200
just add the zeros smarty
Answer:630,200
Step-by-step explanation:
6302x100 is just adding the two zeros from 100 to 6302
please help me with this i really need help
Answer:
the boxes are this
top left: 9
top right is 7
bottom right is 9
Step-by-step explanation: