Answer:
∠ CAB = 60°
Step-by-step explanation:
∠ CAD and ∠ BCA are alternate angles and congruent , so
∠ CAD = 30°
∠ BAD = 90° ( angle in a rectangle ) , then
∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°
The measure of the angle m∠CAB is 60.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The rectangle has 90 degrees on all the vertices.
So,
In ΔABC,
The sum of the angles = 180
So,
30 + 90 + m∠CAB = 180
m∠CAB = 180 - 120
m∠CAB = 60
Thus,
The measure of the angle m∠CAB is 60.
Learn more about rectangles here:
https://brainly.com/question/15019502
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Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2
Answer:
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
Step-by-step explanation:
We have the mean during the interval, which means that the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Lost-time accidents occur in a company at a mean rate of 0.8 per day.
This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.
10 days:
This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]
What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]
[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]
[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]
So
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?
Answer:
12
Step-by-step explanation:
A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1
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Answer:
(b) x = 1
Step-by-step explanation:
A graph shows the solution to f(x) = g(x) is x = 1.
__
We want to solve ...
g(x) -f(x) = 0
x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0
x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping
(x^2 -1)(x +2) +11/3(x -1) = 0 . . . . . . the difference of squares can be factored
(x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor
(x -1)(x^2 +3x +2 +11/3) = 0
The zero product rule tells us this will be true when x-1 = 0, or x = 1.
__
The discriminant of the quadratic factor is ...
b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3
This is less than zero, so any other solutions are complex.
Zoe has 4 pounds of strawberries to make pies. How many ounces of strawberries Is this?
64 oz.
60 oz.
68 oz.
72 oz.
Work Shown:
1 pound = 16 ounces
4*(1 pound) = 4*(16 ounces)
4 pounds = 64 ounces
1. What is the theoretical probability that the family has two dogs or two cats?
2.
Describe how to use two coins to simulate which two pets the family has.
3. Flip both coins 50 times and record your data in a table
like the one below.
Frequency
Result
Heads, Heads
Heads, Tails
Tails. Heads
Tails. Tails
Total
50
4
Based on your data, what is the experimental probability that the family has two dogs or
two cats?
5
If the family has three pets, what is the theoretical probability that they have three dogs or
three cats?
How could you change the simulation to generate data for three pets
6
let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes
h-h, h-t, t-h, t-t.
How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.
2/4 = 1/2
50% is your answer
Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.
Hope this helps you out!
The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?
Answer:
B. 28, 32, 36 millions
Step-by-step explanation:
Given:
P(t) = 24 + 0.4t
Where,
P(t) = population in millions
t = number of years
✔️Value of the population when t = 10:
Plug in t = 10 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(10)
P(t) = 24 + 4
P(t) = 28 million
✔️Value of the population when t = 20:
Plug in t = 20 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(20)
P(t) = 24 + 8
P(t) = 32 million
✔️Value of the population when t = 30:
Plug in t = 30 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(30)
P(t) = 24 + 12
P(t) = 36 million
AABC-AXYZ. What's the scale factor from
AABC to AXYZ?
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Answer:
(d) 1/4
Step-by-step explanation:
The scale factor is the ratio of lengths of corresponding sides:
XZ/AC = 3/12 = 1/4
_____
Additional comment
I find the wording of the question a bit ambiguous. To transform ΔABC to ΔXYZ, every linear dimension of ΔABC is multiplied by 1/4. This is the sense of "ΔABC to ΔXYZ" that is used in the above answer.
On the other hand, one of the ways ratios are written is using the word "to," as in "12 to 3". Using this idea, we might interpret the question to be asking for ...
ΔABC to ΔXYZ = AC to XZ = 12 to 3 = 12/3 = 4
I need help ASAP please no links
Answer: D' = (1, -1)
Step-by-step explanation:
When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).
PLS
Write the equation of the piecewise function that is represented by its graph.
IS IT A, B, C, OR D
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Answer:
a) domain bounds are -1 ≤ x ≤ 1, x > 1
Step-by-step explanation:
In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.
Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.
The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.
The one answer choice that combines these domain descriptions is ...
[tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]
Reasoning by induction
Question 1 options:
1)
develops a general conclusion based on observations of cases.
2)
develops a general conclusion based on given information.
3)
starts with assumptions that are known to be valid to draw another new truths.
4)
uses patterns to create logical proofs.
Answer:
1because the occasion of cases
Based on this example, make a
generalization about the acute angles
formed when two parallel lines are
cut by a transversal.
Answer:
Step-by-step explanation:
There are 4 of them (acute angles that is)Those 4 are less than 90 degrees.They have supplementary angles which are greater than 90 degrees.There are 4 of them also.The total number of angles should be 8 if there are 2 parallel lines and 1 transversal.Please helppppppppp!!!!
Terminal point for 4π/3
(cos4π/3 ,sin4π/3)
{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)
or ,(- 1/2, -√3/2)
OPTION C
Last year Diana sold 800 necklaces. This year she sold 1080 necklaces. what is the percentage increase of necklaces she sold?
Answer:
13.5% is the increase in percentage
Answer:
74%
Step-by-step explanation:
To get the answer, divide 800 by 1080, and you will get a decimal. That decimal is 0.74074074074. Then, move the decimal point two times two the right, so you should have 074.074074074. Ignore everything after the decimal point as well as the 0 before the decimal point, and if done correctly, it should be 74%.
So, the final answer would be 74%.
Hope this helped!
The product of two numbers is 50 and there sum is 15. Find the number.
Answer: the numbers are 10 and 5
Step-by-step explanation:
10 times 5 is 50
10 plus 5 is 15
Please help asap please
Answer:
12.9 miles
Step-by-step explanation:
Formula: (x/360)×dπ(circumference)
90/360=1/4
1/4×16.4π
1/4×51.496
12.874
Answer:
[tex]m JM=90 =\Theta[/tex]
[tex]Radius=dimeter/2=16.4/2[/tex]
[tex]\longrightarrowr=8.2[/tex]
The length of arc JM=
[tex]=\frac{\Theta }{360} \times\pi r[/tex]
[tex]=\frac{90}{360} \times2\times\ 3.14\times 8.2[/tex]
[tex]=12.874[/tex]
[tex]\approx 12.9 \; miles[/tex]
[tex]OAmalOHopeO[/tex]
Describe the system of equations
How many solutions does this system have.
Answer:
Step-by-step explanation:
One solution, at the point of intersection, (3,3)
Simplify
x * x^5 / x^2 * x
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number
How many even numbers can you have?
Answer:
10234
Step-by-step explanation:
one is the smallest number so its first
and then you can place zero
after that just place the second smallest number
and so on
How many counting numbers have three distinct nonzero digits such that the sum of the three digits is 7?
Answer:
6
Step-by-step explanation:
You have 2 conditions.
1. The digits must be different.
2. The digits must add to 7.
There aren't very many
124
142
214
241
412
421
That's it. That's your answer. There are 6 of them
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=12
Step-by-step explanation:
each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle
ex: 8*4=32 and 17*4=68
so we can assume that 15*4= 4x+12
60=4x+12
48=4x
x=12
Answer:
x = 12
Step-by-step explanation:
The triangles are similar so we can use ratios
4x+12 32
------- = ------------
15 8
Using cross products
(4x+12) *8 = 15 * 32
(4x+12) *8 = 480
Divide each side by 8
(4x+12) *8/8 = 480/8
4x+12 = 60
Subtract 12 from each side
4x+12 -12 = 60-12
4x = 48
Divide by 4
4x/4 = 48/4
x = 12
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.1. The study found that for a sample of 1027 teenagers the mean number of energy drinks consumed per week is 5.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
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 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.
The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Solve for x and y…….
The shapes are the same size. Match the sides.
3x -1 = 17
Add 1 to both sides:
3x = 18
Divide both sides by 3:
X = 6
2y = 16
Divide both sides by 2
Y = 8
Answer: x = 6, y = 8
Which one is greater 4.5% or 0.045
Answer:
They are equal
Step-by-step explanation:
4.5% is 0.045 in decimal form
Answer: They are equal
Step-by-step explanation:
I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent (move it two spots to the right).
Function below, choose the correct description of its graph.
vertical
line
horizontal
line
line with a
negative
slope
line with a parabola
positive opening
slope down
O
O
O
O
O
h(x)=0
k(x) = 4x2 +312
f(x) = x-1
O
o
o
O
O
O
Step-by-step explanation:
I think something went wrong with the answer options you provided. and maybe with the problem statement itself.
I see 3 function definitions.
I can tell you what they are and use the provided option phrasing as closely as possible :
h(x) = 0 is a horizontal line (in fact the x-axis)
k(x) = 4x² + 312 is a parabola with the opening upwards
f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)
Last year, the CDC claimed there were 1700 different strains of a virus around the
world. Since then, numbers have increased by 9.7% more than what the scientists
originally estimated. How many strains are estimated currently? Round to the nearest
number.
Answer: 1865
Step-by-step explanation:
Given
Claimed strains of virus is 1700
If it is increased by 9.7%
Estimated value can be given by
[tex]\Rightarrow 1700+1700\times 9.7\%\\\Rightarrow 1700(1+0.097)\\\Rightarrow 1700\times 1.097\\\Rightarrow 1864.9\approx 1865[/tex]
Thus, the estimated number is [tex]1865[/tex]
