Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Tree diagram:
Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow. If he draws one of the pieces without looking, what is the probability of drawing the green before the red?
Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
Find the slope of the line passing through the points (-3, -8) and (4,6).
Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
15 points + brainliest if you can figure this out!
Answer:
(H1, T1)
Step-by-step explanation:
Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).
Answer:
D. (H1, T1)
Step-by-step explanation:
Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is
D. (H1, T1)
HELP number 12 pls i do nor have long more
Answer:
Dian has $250 originally.
Step-by-step explanation:
Let the total money Dian has originally = $S
Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,
Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]
Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]
= [tex]\frac{\text{5S-2S}}{5}[/tex]
= [tex]\frac{3S}{5}[/tex]
Since Dian has $150 left then the equation will be,
[tex]\frac{3S}{5}=150[/tex]
S = [tex]\frac{150\times 5}{3}[/tex]
S = $250
Therefore, Dian has $250 originally.
aryn needs enough mulch to cover a rectangle flower bed measuring 2 1/4 yd by 3 1/2yd each bag cover 3 square yds and cost $4 how many bags does she need and how much money she need
Answer:
cars are dum
Step-by-step explanation:
A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90. its price-earnings ratio equals:
Answer: Price-earnings ratio= 22.0
Step-by-step explanation:
Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90
To find: price-earnings ratio
Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]
Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]
⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]
Hence, the price-earnings ratio= 22.0
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost? A. $205.86 B. $211.50 C. $213.36
Answer:
Barts total cost is (c)213.36
Step-by-step explanation:
First, you subtract 6% from $219
=204.92
add shipping,
+7.50
=213.36
Hope this helps <3
Answer:
C. $213.36
Step-by-step explanation:
The original price is $219 and the discount is 6% which is equal to $13.14
$219 - $13.14 + $7.50 (shipping cost) = $213.36
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
there are three oranges in 200g of bag . if the weight of them with bag is 1.4kg. find the weight of an orange.i want full methods
the bag is 200g
total weight with oranges is 1400g
deduct the bags weight from total weight
1400 - 200
1200g
this is the weight of the three oranges
so each orange would be
1200 ÷ 3
400g
A company has five employees on its health insurance plan. Each year, each employee independently has an 80% probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000.
Calculate the probability that the company's total hospital costs in a year are less than 50,000.
Answer:
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
Step-by-step explanation:
From the given information:
the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.
If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex] probability that this is their last visit.
If zero employee was admitted ;
Then:
Probability = (0.80)⁵
Probability = 0.3277
If one employee is admitted once;
Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]
Probability = 0.2731
If one employee is admitted twice
Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]
Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]
Probability = 0.1820
If two employees are admitted once
Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = 0.0910
∴
the probability that the company's total hospital costs in a year are less than 50,000 = 0.3277 + 0.2731 + 0.1820
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
TRIANGLE ABC IS DILATED BY A SCALE FACTOR OF 0.5 WITH THE ORIGIN AS THE CENTER OF DILATION, RESULTING IN THE IMAGE TRIANGLE A'B'C. IF A=(2,2). IF A (2,2), B= (4,3) AND C=(6,3), WHAT IS THE LENGTH OF LINE B'C'?
Answer: The length of the line B'C" is 1 unit.
Step-by-step explanation:
Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.
If A (2,2), B= (4,3) and C=(6,3).
Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]
Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]
[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]
Length of image = scale factor x length in original figure
B'C' = 0.5 × BC
= 0.5 × 2
= 1 unit
Hence, the length of the line B'C" is 1 unit.
HELPNEEDED.Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.
What is the probability that the pianist will be a boy and the alternate will be a girl?
30%
40%
50%
60%
ASAP PLEASE HELP!!!!!! Find the y-intercept of the rational function. A rational function is graphed in the first quadrant, and in the second, third and fourth quadrants are other pieces of the graph. The graph crosses the x axis at negative 10 and crosses the y axis at negative 2.
Answer:
(0,-2)
Step-by-step explanation:
The y-intercept is simply when the function touches or crosses the y-axis.
We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.
The ordered pair would be (0,-2)
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.
A circle is centered at CC-1, -3) and has a radius of 6.
Where does the point P(-6, -6) lie?
Choose 1 answer:
Inside the circle
On the circle
Outside the circle
Answer:
outside the circle i think
Step-by-step explanation:
Answer:
inside the circle
Step-by-step explanation:
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 6x + 9 = 11
Answer:
x = 3 ± sqrt(11)
Step-by-step explanation:
x^2 - 6x + 9 = 11
Recognizing that this is a perfect square trinomial
(x-3) ^2 =11
Taking the square root of each side
sqrt((x-3) ^2) = ± sqrt(11)
x-3 =± sqrt(11)
Add 3 to each side
x = 3 ± sqrt(11)
Answer:
[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]
Do not hesitate if you have any question
Hope this helps
Which correlation coefficient could represent the relationship in the scatterpot. Beach visitors
Answer:
A. 0.89.
Step-by-step explanation:
The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.
The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.
From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.
Nearsightedness: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) What proportion of children in this sample are nearsighted?
(b) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z statistic).
(d) What is the p-value for this hypothesis test?
(e) What is the conclusion of the hypothesis test?
Answer:
a)the proportion of student is 0.1082
b)
H1: p = .08
H2: p not equal to 0.08
H1: p =0 .08
H2: p < .08
H1: p =0 .08
H2: p >0 .08
c)z=1.45
d) the p value is 0.1470
e)null hypothesis cannot be accepted,There is no enough evidence to reject the null hypothesis.
Step-by-step explanation:
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
given g(x)=3/x^2+2x find g^-1(x)
Answer:
A
Step-by-step explanation:
[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]
Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answer:
lmkjhvjgcfnhjkhbmgnc gfghh
Step-by-step explanation:
3 + 5x, for x = 10
A. 350
B. 120
C. 53
D. 75
Answer:C
Step-by-step explanation:
Pemdas
3+5(10)
5*10=50
3+50=53
Assume production time per unit is normally distributed with a mean 40 minutes and standard deviation 8 minutes. Using the empirical rule, what percent of the units are produced in MORE than 32 minutes?
Answer:
84%
Step-by-step explanation:
We find the z-score here
z= x-mean/SD = 32-40/8 = -1
So the probability we want to find is;
P(z>-1)
This can be obtained using the standard score table
P(z>-1) = 0.84 = 84%
the mean monthly income of trainees at a local mill is 1100 with a standard deviation of 150. find rthe probability that a trainee earns less than 900 a month g
Answer:
The probability is [tex]P(X < 900 ) = 0.0918[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 1100[/tex]
The standard deviation is [tex]\sigma = 150[/tex]
The random number value is x =900
The probability that a trainee earn less than 900 a month is mathematically represented as
[tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]
Generally the z-value for the normal distribution is mathematically represented as
[tex]z = \frac{x -\mu }{\sigma }[/tex]
So From above we have
[tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]
[tex]P(X < 900 ) = P( Z <-1.33)[/tex]
Now from the z-table
[tex]P(X < 900 ) = 0.0918[/tex]
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answer:16.1%
Step-by-step explanation:
Answer:
The investment needs the rate of growth to be approximately 16.1%.
Step-by-step explanation:
Which sequence of transformations on preimage Triangle ABC will NOT produce the image A’B’C’
Answer:
b
Step-by-step explanation:
Find the area of the figure. Round to the nearest tenth if necessary. 386.3m^2 194.3m^2 193.1m^2 201.9m^2
Add the top and bottom numbers together, divide that by 2 then multiply by the height.
15.3 + 19.5 = 34.8
34.8/2 = 17.4
17.4 x 11.1 = 193.14
Answer is 193.1 m^2
Find the surface area of the attached figure and round your answer to the nearest tenth, if necessary.
Answer:
[tex] S.A = 246.6 in^2 [/tex]
Step-by-step explanation:
The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.
Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]
Where,
B.A = Base Area of the pyramid = 9*9 = 81 in²
P = perimeter of the base = 4(9) = 36 in
L = slant height of pyramid = 9.2 in
Plug in the values into the given formula to find the surface area
[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]
[tex] = 81 + 18*9.2 [/tex]
[tex] = 81 + 165.6 [/tex]
[tex] S.A = 246.6 in^2 [/tex]
Is 3 a solution to the equation 6x – 7 = 12?
Answer:
3 is not a solution
Step-by-step explanation:
6x – 7 = 12?
Substitute 3 in for x and see if the equation is true
6*3 - 7 = 12
18-7 = 12
11 =12
This is false so 3 is not a solution
How to do this? what is the answer??
Answer:
I think that is the C
Step-by-step explanation:
Answer:
Option B is the correct answer.
Step-by-step explanation:
here, arc RT =162°
as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.
so, its value must be 81°only.
hope it helps..