Answer:
5
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp /hyp
sin 30 = x / 10
10 sin 30 = x
10 * 1/2 = x
5 =x
A drink contains 20% mango juice and the rest is apple juice. What is the ration of mango juice to apple juice
Answer:
% of apple juice = 100-20 = 80%
mango : apple
= 20 : 80
= 1 : 4
Answer:
1:4
Step-by-step explanation:
20:80 is basically mango to apple juice, so all you have to do is simplify this ratio to the lowest form, which is in fact 1:4
Select all instances in which the variable described is binomial.
a. A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails.
b. A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
c. Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.
d. There are two banking options for customers of ABC Bank, checking or savings. The random variable represents the total number out of 567 customers with a checking account.
e. The probability of drawing an ace in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of ace cards observed.
Answer: a. , c. , d., e.
Step-by-step explanation:
A variable that counts how many times a certain event occurs in a particular number of trials is known as binomial random variable.
For each trial, there exist only two outcomes .
The probability of for each event is the same on each trial.
a. Event has two outcomes with same probability as 0.50, therefore the random variable represents the total number of flips required to get tails is a binomial random variable.
b. Total guidelines are 5.
Here total outcomes are not 2 , it does not meet with the conditions of binomial.
c. The random variable represents the total number of children from this pair of parents with blue eyes has two outcomes (where has or not.)
also, the probability of having blue eyes is same in each trial, so it represents binomial random variable.
d. The random variable represents the total number out of 567 customers with a checking account has two outcomes (checking or savings).
So, it represents binomial random variable.
e. The random variable represents the total number of ace cards observed has two outcomes ( ace or not ace).
So it represents the binomial random variable.
Solve this inequality 15n<8n-21
The solution of the inequality 15n>8n-21 is given by, n<-3.
Inequality is a relation between two or more mathematical expression or quantities via unequal signs i.e. greater, less, greater or equal, less or equal, not equal.
Given that the inequality is 15n<8n-21
Solving the inequality we have,
15n<8n-21
15n-8n<8n-21-8n, subtracting from both sides
7n<-21
n<-3, dividing 7 from both sides
So the solution of the given inequality is, n<-3.
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Can somebody please help?? i’ll give Brainliest to whoever answers first.
There are 625 students in Leon's school. He takes a random sample of 75 students from the entire school population. In the sample, 33
students are planning to attend the end of year picnic.
Based on his data, how many students from the entire school are planning to attend the end of year picnic? Show ALL your work!
Answer:
The answer is 275 students.
Step-by-step explanation:
In 75 students, 33 students attend.
So the ratio is 33/75.
so multiply with 625.
625 x 33/75 = 275
What is the value of w?
Answer:
amgle sut is equal to angle suv bcz of sas criteria . so 10+w = 3w
on solving we get w= 5
Here is a table classifying 116 thousand US households (in thousands) in
2013 by tenure and insurance status:
Insurance status Owns home Rents home
Insured
71
13
Uninsured
27
5
Find the relative frequency marginal distribution of insurance status.
Round to the nearest whole percent.
Insured: %
Uninsured: %
Insured = 72%.
Uninsured = 28%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Here is a table classifying 116 thousand US households (in thousands) in
2013 by tenure and insurance status:
Insurance status Owns home Rents home
Insured 71 13
Uninsured 27 5
Total house = 71 + 13 + 5 + 27 = 116
Insured = (71 + 13)/116 = 72%.
Uninsured = (5 + 27)/116 = 28%.
Therefore, 72% = insured and 28% = uninsured.
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) Find the sum to infinity of the sequence 1, 1/4, 1/16, 1/64.
The sum of the terms till infinity of the sequence 1, 1 / 4, 1 / 16, 1 / 64 will be 4 / 3.
We have the sequence:
1, 1 / 4, 1 / 16, 1 / 64.
Initial term = a
a = 1
Common ratio = d
d = 1 / 4
The formula for the sum of the terms to infinity is given by:
S_∞ = a / (1 – r)
S_∞ = ( 1 ) / (1 – 1 / 4)
S_∞ = 1 / ( 3 / 4 )
S_∞ = 4 / 3
Therefore, we get that, the sum of the terms till infinity of the sequence 1, 1 / 4, 1 / 16, 1 / 64 will be 4 / 3.
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Please help me!A bag holds 5 pounds of pet food. If Paul uses the 5 pounds of food to fill 6 plastic containers equally, how much pet food will each container hold?0.830.80.8030.83
We must divide the 5 pound bag in 6 different containers, therefore:
\(\frac{5}{6}=0.83\)Each container will hold 0.83 pet food
find the area of a rectangle with a length of 10 inches and a width of 4 inches
Answer:
40 in²---------------------
Formula for area of a rectangle with dimensions l and w is:
A = lwSubstitute 10 for l and 4 for w:
A = 10*4A = 40 in²Circle 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°.
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Describe a series of transformations that moves the blue figure to the red figure Be specific! If there is a : Translation - show number and direction Reflection - give axis of reflection Rotation - give direction (clockwise or counterclockwise) and degree amount
The blue figure is moved 5 units to the right (T(5, 0)), reflected in the y-axis (r(y-axis)), and then rotated 90 degrees counterclockwise (R(-90)).
Translation: Move the blue figure 5 units to the right (translation of 5 units to the right, denoted as T(5, 0))
Reflection: Reflect the figure in the y-axis (denoted as r(y-axis))
Rotation: Rotate the figure 90 degrees counterclockwise (denoted as R(-90))
The series of transformations that moves the blue figure to the red figure is T(5, 0) followed by r(y-axis) followed by R(-90).To better understand this, let's break down the transformations. The first transformation is a translation, which is a movement of a figure from one location to another. In this case, the figure is being moved 5 units to the right. This is denoted as T(5, 0).The second transformation is a reflection, which is a flip of a figure over a line or axis. In this case, the figure is being reflected in the y-axis. This is denoted as r(y-axis).The third transformation is a rotation, which is a turn of a figure around a point. In this case, the figure is being rotated 90 degrees counterclockwise. This is denoted as R(-90).Therefore, the series of transformations that moves the blue figure to the red figure is T(5, 0) followed by r(y-axis) followed by R(-90).
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Which of the following is a vertical line?
1) y = 6
2) x = 6
3) y = 6x - 4
4) y = -x
Answer:
2) x = 6
Step-by-step explanation:
A vertical line is a line that goes up and down, where x goes not change
It is of the form x=
x =6 is a vertical line
Answer:
It is 2) x=6
Step-by-step explanation:
Since the x axis is the vertical side, it would be vertical. The line would also be vertical, the others are horizantal and are not vertical.
1. a. Provide two independent events that you know the probability of.
b. Explain how you know these events are independent.
c. Find the probability that they both occur.
2. a. Provide two dependent events.
b. Explain how you know these events are dependent.
c. Explain why these dependent events might require a different method for calculating the probability of both events occurring.
Example of dependent events and independent events and their probabilities are as given below.
How to provide two independent events with known probability?1. a. Two independent events that I know the probability of are:
Rolling a fair die and getting a 4 (probability of 1/6)
Flipping a fair coin and getting heads (probability of 1/2)
b. I know these events are independent because the outcome of one event does not affect the outcome of the other event. The outcome of rolling a die does not affect the outcome of flipping a coin, and vice versa.
c. The probability of both events occurring is (1/6) × (1/2) = 1/12
2a. Two dependent events:
i. Drawing a red card from a deck of cards and then drawing another card (without replacement)
ii. Drawing a red ace and then drawing another red card (without replacement)
b. I know these events are dependent because the outcome of the first event affects the outcome of the second event. The probability of the second event depends on the outcome of the first event.
c. These dependent events might require a different method for calculating the probability of both events occurring, such as conditional probability.
The probability of both events occurring would be P(A and B) = P(A) × P(B|A)
where P(A) is the probability of the first event and P(B|A) is the probability of the second event given that the first event has occurred.
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Which ordered pair is a solution to the equation?
4y = -7x-5
(2,-2)
(1.3)
(-5,0)
(-3, 4)
Answer:
Step-by-step explanation:
4(4) = -7(-3) - 5
16 = 21 - 5
16 = 16
answer is D
Answer: (-3.4)
Step-by-step explanation: took test 6.02
Foundations wrap up Systems of Equations
Use Newton’s method to approximate the indicated root of the equation correct to six decimal places. The positive root of 3 sin x = x
Answer:
\(x \approx 2.278863\)
Step-by-step explanation:
Required
The positive root of \(3\sin(x) = x\)
Equate to 0
\(0 = x -3\sin(x)\)
So, we have our function to be:
\(h(x) = x -3\sin(x)\)
Differentiate the above function:
\(h'(x) = 1 -3\cos(x)\)
Using Newton's method of approximation, we have:
\(x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}\)
Plot the graph of \(h(x) = x -3\sin(x)\) to get \(x_1\) --- see attachment for graph
From the attached graph, the first value of x is at 2.2; so:
\(x_1 = 2.2\)
So, we have:
\(x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}\)
\(x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}\)
\(x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641\)
The process will be repeated until the digit in the 6th decimal place remains unchanged
\(x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654\)
\(x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627\)
\(x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627\)
Hence:
\(x \approx 2.278863\)
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you can compare the length of sides of both the triangles...
Answer:
see explanation
Step-by-step explanation:
We can show that Δ ABC and Δ DEF are similar by the SSS postulate
If the ratios of the 3 pairs of corresponding sides are equal , then the triangles are similar.
\(\frac{AB}{DE}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\)
\(\frac{AC}{DF}\) = \(\frac{8}{12}\) = \(\frac{2}{3}\)
\(\frac{BC}{EF }\) = \(\frac{5}{7.5}\) = \(\frac{2}{3}\)
Then by the SSS postulate the triangles are similar
Since the triangles are similar then corresponding angles are congruent, so
∠ D = ∠ A
in a large bag of marbles, 20% of them are red. A child chooses 14 marbles from his bag. If the child uses the marbles at random what is a chance that the child gets less than six red marbles?
If the child uses the marbles at random what is the chance that the child gets less than six red marbles is given as 0.9561. See the calculation below.
Note that we are given the following:
p = 20% = 0.20
1 - p = 1 - 0.20 = 0.80
n = 14
Utilizing the binomial formula, we have:
P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x
P(X < 6) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)+ P(x = 4) + P(x = 5)
Plugging in the value of n, we have:
= ((14! / 0! (14)!) * 0.200 * (0.80)14 + ((14! / 1! (13)!) * 0.201 * (0.80)13 + ((14! / 2! (12)!) * 0.202 * (0.80)12 + ((14! / 3! (11)!) * 0.203 * (0.80)11 + ((14! / 4! (10)!) * 0.204 * (0.80)10 + ((14! / 5! (9)!) * 0.205 * (0.80)9
= 0.9561
As a result, the probability that the youngster would receive less than six red marbles is provided as 0.9561 if the marbles are used at random.
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X3-x-9=0 bisection method
Step-by-step explanation:
The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].
Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.
Now we can apply the bisection method as follows:
Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.
Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.
Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.
Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.
Evaluate f© ≈ 1.765625.
Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.
We can continue this process until we reach the desired level of accuracy.
the vector is a linear combination of the vectors and if and only if the matrix equation has a solution , where and .
The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.
We first thought of a matrix as a rectangular array of numbers. When the number of rows is m and columns is n, we say that the dimensions of the matrix are m×n.
A vector is most simply thought of as a matrix with a single column. There are two operations we can perform with vectors: scalar multiplication and vector addition. Both of these operations have geometric meaning.
Given a set of vectors and a set of scalars we call weights, we can create a linear combination using scalar multiplication and vector addition.
The product of two matrices can be seen as the result of taking linear combinations of their rows and columns. This way of interpreting matrix multiplication often helps to understand important results in matrix algebra.
The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.
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Please help if u care pls
1/4x+5/2x-2=4-1/4x
What is the value of x
Answer: The correct answer is: [A]:
__________________________________________________
" Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
__________________________________________________
Step-by-step explanation:
__________________________________________________
Note that the "unit rate" is the term that refers to:
a "quantity" / or "quantitative value" ;
→ of some type of "countable units"
{e.g. "currency" — [such as: dollars, cents, pounds] ; "distance/length/ width/ height" — [such as: miles, kilometers, meters, centimeters, yards, feet, inches] ; pieces of fruits — [such as: number of apples; cans of soda, number of red dresses] ;
__________________________________________________
per "single unit" of something — {e.g. per hour; per minute; per mile; per ounce; per hour; per dollar, per kilometer, per day, per week.
{e.g.
→ " 3 apples eaten per [single] apricot eaten" ;
→ " 46 miles per hour.
→ " 8.3 cents per oz." ;
→ " 5 Liters of soda per dollar " ;
→ " 2.3 grams per mole " ;
→ " 4.6 mg solute / kg of solvent " ;
→ " 5 km / hr " ; {that is: " 5 km per hr " } .
→ " 3 yds. per [single] square inch."
→ " 35 parts per hundred" ; {that is: " 35 percent" ; or: " 35 % " . } .
→ " ... The cilantro is on sale for 33 cents per bundle ...} ."
→ ... to provide a few examples.
__________________________________________________
On on Cartesian plane graph, the "x-axis" is located on the "horizontal axis" that represents the "independent variable" (or, at times, the "experimental value" — which can be manipulated — or "controlled" —or be subjected to being "manipulated" / "controlled" / or, "selected".
The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .
So, if the "unit rate" represents the "single unit rate" ; we look at "x = 1 " ; since we are "choosing" this particular "single" rate of per "single" (i.e. "1" ) ; so we do not have a choice in what "y-value" of the particular graph to select. We can control the fact that we are "choosing" to find the "unit" rate, so we select the "independent variable" , "x = 1 " . We then examine the "corresponding y-value" that happens to exist when "x = 1 " .
{Note that we have "no control" over what that "y-value" is ; at the: "[point which: " x = 1 .] . "
_________________________________________________
→ As such, that "y-value" [insert that numeric "y-value" ; followed by the units represented by the "y-axis" ] ;
per " 1 " [insert "single unit" represented by the "x-axis" ] ;
_________________________________________________
→ is the: "unit rate" .
__________________________________________________
So:
The correct answer is: [A]:
__________________________________________________
" Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
Answer:
Step-by-stbhubhbhnhnkjnkjnep explanation:
What is (I^2)+(I^2)+3x if x=I^2?
Show your work.
Answer:
-5
Step-by-step explanation:
(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5
Given that the diameter of Circle A is 7 cm, and the radius of Circle B is 21 cm, what can be concluded about the two circles?
A.
the circles are similar and congruent
B.
the circles are neither similar nor congruent
C.
the circles are similar
D.
the circles are congruent only
C. the circles are similar
Given radius:Circle A = 7 cm
Circle B = 21 cm
1) Similar Shape : they can be enlarged and diminished where size varies.
2) Congruent Shape : they must have similar size and lengths.
Hence, here the circles are similar with different lengths.
x = 3 / 5 (cb+k)
Solve for b
Answer:
(5/3 x - k)/c =b
Step-by-step explanation:
x = 3 / 5 (cb+k)
Multiply each side by 5/3
5/3x =5/3* 3 / 5 (cb+k)
5/3x = (cb+k)
Subtract k
5/3 x - k = cb +k-k
5/3 x - k = cb
Divide by c
(5/3 x - k)/c = cb/c
(5/3 x - k)/c =b
Find the slope of the line.
Answer:
slope = 3
Step-by-step explanation:
rise/run = 3/1 = 3
9
8
a
+
4
8
a
−
5
8
8
9
a+
8
4
a−
8
5
A
138a−58
8
13
a−
8
5
B
58a−58
8
5
a−
8
5
C
811a+14
11
8
a+
4
1
D
78a+85
8
7
a+
5
8
Which explains how you round 212.809 to the nearest hundredth?
A.
Since the digit in the hundredths place is less than 5, keep the digit in the hundredths place. Then drop the digit in the thousandths place.
B.
Since the digit in the hundredths place is less than 5, keep the digit in the tenths place. Then drop the digit in the hundredths and thousandths places.
C.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
D.
Since the digit in the thousandths place is greater than or equal to 5, keep th
Answer:
c
Step-by-step explanation:
Right triangle 10 fr and 6ft what is the area of the right triangle
Answer:
60ft is the area
Step-by-step explanation:
HAVE FUN IN UR LIFE!
Answer:
the area is 44
Step-by-step explanation:
10x2=20+12=32+12=44
F(x) = 2x-(x+6) for f(-3)
ZABD and ZDBC are supplementary angles.
What is the measure of x?
x = [?]
DK
X 148°
AR
>C
>C
B
Angles are not drawn to scale.
Enter
Answer:
Solution given:
x+148=180°[linear pair]
x=180°-148=32°
x=32° is your answer
Step-by-step explanation:
solution :
Given,
X+48 °= 180° [ being linear pair ]
X=180°-48°
X=32°
so,
X=32° answer.
hope it is helpful to you ☺️
Eve and Patty swam fewer laps than Maureen. Patty swam more laps than Eve, and Maureen swam fewer laps than Raymond. Who swam the most laps?
Answer:
Raymond
Step-by-step explanation:
1 ) Eve and Patty swam fewer laps than Maureen so...
Eve and Patty < Maureen
2 ) Patty swam more laps than Eve...
Patty > Eve
3 ) Maureen swam fewer laps than Raymond...
Maureen < Raymond
4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...
Maureen and Raymond
5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.
Raymond
6 ) This mean that the one who swam the most laps is...
Raymond
Hope this helps! :)