Answers
Answer:
x = 3
Step-by-step explanation:
First, use trigonometric function to find RT.
θ = 60°
Opposite = 2√3
Hypotenuse = RT
Apply SOH:
Sin θ = Opp/Hyp
Plug in the values
Sin 60° = 2√3/RT
RT*Sin 60° = 2√3
Divide both sides by Sin 60°
RT = 2√3/sin 60°
RT = 2√3 × √3/2 (sin 60° = √3/2)
RT = (2√3 × √3)/2
RT = (2 × 3)/2
RT = 3
✔️Find x
θ = 45°
Opposite = x
Adjacent = 3
Apply TOA:
Tan θ = Opp/Adj
Substitute
Tan 45° = x/3
3 × Tan 45° = x
3 × 1 = x (tan 45° = 1)
3 = x
x = 3
Related Questions
which expression is equivalent to c^2 - 4 / c + 3 /
Answers
Step-by-step explanation:
[tex] \frac{ {c}^{2} - 4 }{c + 3} [/tex]
[tex] \frac{(c - 2)(c + 2)}{(c + 3)} [/tex]
7. A 6 litre jug of lemonade contains 1.6 litres of lemon juice and the rest is water. How much lemon juice does a 1.5 litre bottle of lemonade contain?
Answers
Answer:
5.625 litres
Step-by-step explanation:
1. We have to find how many litres of of lemon juice does a 1 litre jug of lemonade contains :
6 litres ÷ 1.6 litres = 3.75 litres
2. How many litres of lemon juice does a 1.5 litre bottle of lemonade contain?
= 3.75 litres × 1.5 litres
= 5.625 litres #
Answer:
A 1.5 litre bottle of lemonade contains 0.4 litre of lemon juice
Step-by-step explanation
let x be the litre of lemon juice in 1.5 litre of lemonade
litre of lemon juice in 6 litre of lemonade = 1.6
so , [tex]\frac{6}{1.6} = \frac{1.5}{x}[/tex]
x = [tex]\frac{1.5 * 1.6}{6}[/tex]
x=[tex]\frac{2.4}{6}[/tex]
x = 0.4 litre
help fast I'm dum
and I'm sorry if I keep spamming this.
Curtis types 48 words in 1 minute how many words does Curtis type in 8 minutes? use the following equivalent rates to help solve the problem. how many words does Curtis type in 8 minutes?
Answers
Answer:
384
Step-by-step explanation:
Answer:
384 words
Step-by-step explanation:
Number of words typed in 1 minute = 48
So, number of words typed in 8 minutes
= Number of words typed in 1 minute × 8
= 48 × 8
= 384
So, Curtis types 384 words in 8 minutes.
11. The coordinates of AABC are A(-1,1), B(3,3),
and C(4, -2). Find the coordinates of points A', B',
and C' under the translations that take
a. P(0,0) to Q(1,3)
b. P(0, -1) to Q(4,-2)
c. P(-1,-2) to Q(-2,2)
Answers
Answer:
See explanation
Step-by-step explanation:
Given
[tex]A = (-1,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]C =(4,-2)[/tex]
Solving (a): [tex]P(0,0) \to Q(1,3)[/tex]
This means that:
[tex](x,y) \to (x+1,y+2)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1 + 1,1+2)[/tex]
[tex]A' = (0,3)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3 + 1,3+2)[/tex]
[tex]B'= (4,5)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+1,-2+1)[/tex]
[tex]C' = (5,-1)[/tex]
Solving (b): [tex]P(0,-1) \to Q(4,-2)[/tex]
This means that:
[tex](x,y) \to (x+4,y-1)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1+4,1-1)[/tex]
[tex]A' = (3,0)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3+4,3-1)[/tex]
[tex]B'= (7,2)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+4,-2-1)[/tex]
[tex]C' = (8,-3)[/tex]
Solving (c): [tex]P(-1,-2) \to Q(-2,-2)[/tex]
This means that:
[tex](x,y) \to (x-1,y)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1-1,1)[/tex]
[tex]A' = (-2,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3-1,3)[/tex]
[tex]B'= (2,3)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C'= (4-1,-2)[/tex]
[tex]C'= (3,-2)[/tex]
Someone help me!!! Help
Answers
Answer B.ED
Step-by-step explanation:
A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.17 ounce. The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)
Answers
Answer:
The company should use a mean of 12.37 ounces.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.17 ounce.
This means that [tex]\sigma = 0.17[/tex]
The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)?
This is [tex]\mu[/tex], considering that when [tex]X = 12[/tex], Z has a p-value of [tex]1 - 0.985 = 0.015[/tex], so when [tex]X = 12, Z = -2.17[/tex].
Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.17 = \frac{12 - \mu}{0.17}[/tex]
[tex]12 - \mu = -2.17*0.17[/tex]
[tex]\mu = 12 + 2.17*0.17[/tex]
[tex]\mu = 12.37[/tex]
The company should use a mean of 12.37 ounces.
find the value of x in 81^x=1/3?
Answers
Answer:
x = -1/4
Step-by-step explanation:
[tex]81^{x}[/tex] = 1/3
[tex]3^{4}^{x}[/tex] = [tex]3^{-1}[/tex]
4x = -1
x = -1/4
Answer:
x = - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex]81^{x}[/tex] = [tex]\frac{1}{3}[/tex] [ note that 81 = [tex]3^{4}[/tex] ] , then
[tex](3^4)^{x}[/tex] = [tex]3^{-1}[/tex] , that is
[tex]3^{4x}[/tex] = [tex]3^{-1}[/tex]
Since the bases on both sides are equal, both 3, then equate exponents
4x = - 1 ( divide both sides by 4 )
x = - [tex]\frac{1}{4}[/tex]
If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?
Answers
Answer:
The cube root parent function:
f(x) = [tex]\sqrt[3]{x}[/tex]Horizontally stretched by a factor of 4:
g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]Translated 5 units right:
h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]Translated 3 units up:
k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]If f(x) = 3x-1 and g(x)= x+2 find (f-g) (x)
Answers
Answer:
2x-3
Step-by-step explanation:
f(x) = 3x-1
g(x)= x+2
(f-g) (x) = 3x-1 - (x+2)
Distribute the minus sign
= 3x-1 -x-2
Combine like terms
= 3x-x -1-2
=2x -3
What is the slope of a relation with ordered pairs of (-5, 3) and (4.1).
9/2
2/9
-9/2
-2/9
2
-2
Answers
2/-9
-2/9 is the answer
Solve 5 (2x + 1 ) + 4 = 6 ( 3x + 2) - 7
Answers
5(2x+1)+4=6(3x+2)-7
10x+5+4=18x+12-7
10x-18x=12-7-5-4
-8x=-4 (-1)
8x=4
x=4/8 (/4)
x=1/2
Answer:
x = 1/2
Step-by-step explanation:
5(2x + 1) + 4 = 6 (3x + 2) - 7
~Simplify both sides
10x + 9 = 18x + 5
~Subtract 9 from both sides
10x = 18x - 4
~Subtract 18x to both sides
-8x = -4
~Divide -8 to both sides
x = 1/2
Best of Luck!
A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is
where the deviations ε i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ . This model was fit to the data using the method of least squares. The following results were obtained from statistical software:
R 2 =0.423, s=2.2018
The quantity s = 2.2018 is an estimate of the standard deviation, σ, of the deviations in the simple linear regression model. The degrees of freedom for s are
a.) 100
b.) 99
c.) 98
d.) 2
Answers
Answer:
C. 98
Step-by-step explanation:
The proposed regression equation is weight = b + width * m
R2 = 0.423
A.) What is the regression equation for this example?
The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963
In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:
^Y= 2.3013 + 0.7963Xi
B.) What is the explanatory, or predictor, variable in this study?
The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:
X: Width of a horseshoe crab (cm)
C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.
To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.
The hypotheses are:
H₀: β=0
H₁: β≠0
α: 0.05
The value of the statistic under the null hypothesis is t= 8.48
D.) What can we say about the p-value?
This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:
P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001
E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?
As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:
Critical values ± = ± = ± 1.984
This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-
F.) Find the confidence interval for the slope.
Using a 95% confidence level, the interval for the slope is:
[m ± Sm]
[0.7963 ± 1.984 * 0.0939]
[0.61; 0.98]
G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.
Yes, there is a significant relationship between the width and weight of the horseshoe crabs.
Using the critical value approach:
The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.
If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.
what is 5 2/3 - 11 1/6
Answers
Answer:
Check the photo for the answer
5.
A number is squared, then multiplied by 6. The result is 54. What was the number?
Answer:
Answers
Answer:
± 3
Step-by-step explanation:
let n be the number then the number squared is n² , so
6n² = 54 ( divide both sides by 6 )
n² = 9 ( take the square root of both sides )
n = ± [tex]\sqrt{9}[/tex] = ± 3
That is the number is 3 or - 3
Identify the coordinates of the point shown. An image of a coordinate plane with one point plotted. It is 3 units to the left of the y-axis and 6 units below the x-axis. Question 23 options: (−6, 3) (−6, −3) (−3, −6) (3, −6)
Answers
Answer:
(-3, -6)
Step-by-step explanation:
always start from the origin! Hope this helps!
Point C partitions AB into two parts so that the ratio of the length of AC to the length of CB is 1:5. What are the coordinates of point ?
Select and drag a number to each empty box to correctly complete the coordinates of point
The coordinates of point C are?
Answers
9514 1404 393
Answer:
C(-1, -4)
Step-by-step explanation:
We want ...
AC/CB = 1/5
5(C-A) = B-C . . . . multiply by 5CB
6C = B +5A . . . . . add 5A-C
C = (B +5A)/6 . . . divide by 6
C = ((4, 6) +5(-2,-6))/6 = (4-10,6-30)/6 = (-6, -24)/6
C = (-1, -4)
How many sides does a regular polygon have if each interior angle measures 178°?
Answers
The number of sides of a regular polygon with an interior angle [tex]\[{178^ \circ }\][/tex] is 180.
What is the regular polygon?
A polygon is regular when all angles are equal and all sides are equal.
A regular polygon has if each interior angle.
Interior angle of given polygon =178
An exterior angle of polygon =180 −178 =2
The sum of exterior angles of any polygon is 360
Number of sides of a regular polygon
[tex]=\frac{360}{2}[/tex]
[tex]=180[/tex]
Therefore, The number of sides of a regular polygon is 180.
To learn more about the side of regular polygon visit:
https://brainly.com/question/1592456
Find formulas for X, Y, and Z in terms of A, B, and C. It may be necessary to make assumptions about the size of a matrix in order to produce a formula.
[A B C 0] [1 0 X Y] = [0 1 Z 0]
Find the formulas for X, Y, and Z. Note that I represents the identity matrix and 0 represents the zero matrix.
Answers
Answer:
Here the answer is given as follows,
Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain?
Answers
Answer:
28 blue marbles
Step-by-step explanation:
yellow: blue
8 4
To get to 56 yellow marbles multiply by 7
yellow: blue
8*7 4*7
56 28
There will be 28 blue marbles
Eli had mini-golf scores of -3, -4, and -3. What was his total score for the three rounds?
Answers
Answer:-10
-3+-4+-3
-3-4=-7
-7+-3=-7-3
=-10
3/4 pound of Colby cheese costs $1.69. Find the unit price per pound. (3/4 pound=12)
Answers
Answer:
2.25
Step-by-step explanation:
We can write a ratio to solve
1.69 x
------ = ---------------
3/4 lb 1 lb
Using cross products
1.69 * 1 = 3/4 *x
1.69 = 3/4 x
Multiply by 4/3
1.69 * 4/3 = x
x=2.25333
Rounding to the nearest cent
Mark earns $47,800 a year working for a delivery service. He is single and pays $2,152.60 in state income tax each year. He claims no dependents. What is the tax rate of Mark’s state he lives in?
Answers
Answer:
4.5%
Step-by-step explanation:
The tax rate=(2152.6/47800)*100=4.5%
A parallel plate capacitor has an area of 1.5 cm
2
and the plates are separated a distance of 2.0 mm with air between them. How much charge does this capacitor store when connected to a 12V battery?
Answers
Step-by-step explanation:
Given:
[tex]A=1.5\:\text{cm}^2×\left(\frac{1\:\text{m}^2}{10^4\:\text{cm}^2}\right)=1.5×10^{-4}\:\text{m}^2[/tex]
[tex]d = 2.0\:\text{mm} = 2.0×10^{-3}\:\text{mm}[/tex]
The charge stored in a capacitor is given by [tex]Q = CV.[/tex] In the case of a parallel-plate capacitor, its capacitance C is given by
[tex]C = \epsilon_0\dfrac{A}{d}[/tex]
where [tex]\epsilon_0[/tex] = permittivity of free space. The amount of charge stored in the capacitor is then
[tex]Q = \left(\epsilon_0\dfrac{A}{d}\right)V[/tex]
[tex]\:\:\:\:\:=\left[\dfrac{(8.85×10^{-12}\:\text{F/m})(1.5×10^{-4}\:\text{m}^2)}{(2.0×10^{-3}\:\text{m})}\right](12\:\text{V})[/tex]
[tex]\:\:\:\:\:=8.0×10^{-12}\:\text{C}[/tex]
what is 98×63-32×69=
Answers
Answer: plz marl brainilist
3966
Step-by-step explanation:
(98 × 63 - 32 × 69
98 * 63) - (32 * 69)
3966
Step-by-step explanation:
98 x 63 - 32 x 69 =
Multiply
6174 - 2208
Subtract
3966
write an absolute value equations to satsify the given solution set shown on a number line -1/2 1/2 and a
Plz help fast
Answers
9514 1404 393
Answer:
|x| = 1/2
Step-by-step explanation:
Perhaps the simplest equation is ...
|x| = 1/2
__
You could get more elaborate:
|2x| = 1
3 -|6x| = 0
Use the distributive property to remove the parentheses.
I’m so bad at math so I need help :/
Answers
27x^5 + 30x^4
Step-by-step explanation:
Multiply 3x^3 out of (9x^2 + 10x)
Step 1. Multiply 3x^3 x 9x^2
Answer: 27x^5
Step 2. Multiply 3x^3 x 10x
Answer: 30x^4
“Add these two products together”
27x^5 + 30x^4
Hope this helps!
Love you.
- doomdabomb
hola soy nuevo, y quisiera saber como funciona brainly.com, porque yo siempre e utilizado brainly.lat, pero me e cambiado para este.
Answers
Answer/Step-by-step explanation:
Hola amigo. Mucho gusto. En Brainly.com puede responder a sus preguntas y obtener explicaciones exhaustivas. Esto le permite aprender de forma más inteligente.
Y... yo hablo pequeno español.
Student is 19 years old in the world has a population of 6.7 billion assuming that the population continues to grow in annual rate of 1.1%, predict what the worlds population will be when the student is 52
Answers
9514 1404 393
Answer:
9.6 billion
Step-by-step explanation:
The population multiplier is 1+1.1% = 1.011 each year. After 52-19 = 33 years, the multiplier will be 1.011^33 ≈ 1.4348.
When the student is 52, the population of the world will be about ...
6.7 billion × 1.4348 ≈ 9.6 billion
The five number summary of a dataset is given as
0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
.
.
Answers
Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]
An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]
Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].
Now,
[tex]IQR=14-4[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].
Now,
[tex]IQR=18-8[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.
You can often use geometric figures to model objects in the real world. You can transfer your knowledge of the properties of these figures to better understand and describe the objects that they represent. For each shape the table, list three examples of real-world objects that could be modeled by the shape. Use your experiences, the Internet, newspapers, magazines, or other resources to uncover examples.
Answers
Geometric figures are basically figures that have a boundary. The geometric figures and their real life examples are:
Rectangular prism: Building block, Gift box, CabinetTriangular prism: Tomblerone, Triangular roofs, Camping tentsCylinder: Pencil holders, Toilet paper rolls, Drink cansCone: Funnel, Party hat, Traffic conePyramid: Pyramids of Egypt, Pyramid roof, Pyramid tentsSphere: Soccer ball, Golf ball, PlanetsTo determine the real life object of each geometric figure, we simply identify objects that have similar features as the geometric figure.
For instance, a rectangular prism has 6 rectangular faces; building blocks, some gift box and cabinets also have 6 rectangular faces.
So, these three real life objects can be used as examples of a rectangular prism.
When the above explanation is applied to the other geometric figures, we come up with the following list:
Triangular prism: Tomblerone, Triangular roofs, Camping tentsCylinder: Pencil holders, Toilet paper rolls, Drink cansCone: Funnel, Party hat, Traffic conePyramid: Pyramids of Egypt, Pyramid roof, Pyramid tentsSphere: Soccer ball, Golf ball, PlanetsRead more about geometric figures at:
https://brainly.com/question/8430622
In the photo are a couple possible answers you could use.
