In a parallelogram, two adjacent sides measure 20 cm and 27 cm. The shorter diagonal is 23 cm. Determine, to the nearest degree, the measure of the larger angles in the parallelogram.
If two adjacent sides of parallelogram are 20 cm and 27 cm and the shorter diagonal is 23 cm then the measure of larger angles in the parallelogram is 123.75°.
Given Two adjacent sides are 20 cm and 27 cm. The shorter diagonal is 23 cm. and we need to find the measure of larger angle.
From law of cosines
[tex]c^{2} =a^{2} +b^{2} -2abcos d[/tex]
where c is the opposite side of angle, a and b are other sides and d is the angle.
[tex]23^{2} =20^{2} +27^{2} -2*20*27cos d[/tex]
where 23 is the length of shorter diagonal
529=400+729 - 1080 cos d
1080 cos d=600
cos d=600/1080
cos d=0.55
d=[tex]cos^{-}[/tex]0.55
d=56.25°
Adjacent angle=180-56.25
=123.75°
Largest angle=123.75°.
Hence the larger angle of parallelogram having sides 20 and 27cm is 123.75°.
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If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P (more than 9) with n=12 and p= 0.3 by using the normal distribution as an approximation to the binomial distribution, if np<5 or nq<5, then state that the normal approximation is not suitable
The normal approximation is not suitable as np<5.
Given,
mean = np
It turns out that if np and nq are both at least 5, the normal distribution can be used to approximate the binomial distribution. Additionally, keep in mind that a binomial distribution has a mean of np and variance of npq.
Hence apply the mean formula and get the value for np
n= 12 and p=0.
therefore mean = np
np = n×p
np = 12×0.3×
np = 3.6
np is less than 5.
nq=?
q=1-p
q=1-0.3
q=0.7
∴nq = 12 × 0.7
nq = 8.4
nq is not less than 5
It's remarkable that the normal distribution may accurately represent the binomial distribition when n, np and nq are large.
since here only nq is greater than five and np is less than five, therefore we conclude that normal approximation is not suitable.
Hence np<5 so normal approximation is not suitable.
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2. How is the graph of g(x)=x³-1 related to the graph
of f(x)=x³?
A. The graph of g(x) is a translation of the
graph of f(x) down 1 unit
B.
The graph of g(x) is a translation of the
graph of f(x) down 1 unit and a reflection
across the x-axis.
C. The graph of g(x) is a translation of the
graph of f(x) left 1 unit and a reflection
across the y-axis.
Answer:
[tex]A[/tex]
Step-by-step explanation:
Indeed, the graph of [tex]f(x)[/tex] underwent only one change:
[tex]f(x) = x^3 \Leftrightarrow g(x) = f(x) - 1 = x^3 - 1[/tex].
Take a look at the attachments in order to follow the process.
Need help with this one can anyone help me?
See question below super confused
Answer:
$ 1021.25
Step-by-step explanation:
FV = P ( 1 + .085 * 3/12) = 1021.25
3/12 = 3 months out of a year
.085 = decimal interest P = 1000
The one-to-one functions g and h are defined as follows.
The value of g⁻¹(5) = 0, h⁻¹(x) = (x+10)/3, and the value of h(h⁻¹(5)) = 5 if g = {(-4, 1), (0, 5), (5, -3), (8, -8)} and h(x) = 3x - 10
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
g = {(-4, 1), (0, 5), (5, -3), (8, -8)}
As we know,
If f(x) has an ordered pair (x, y) then its inverse of a function has (y, x).
g⁻¹ = {(1, -4), (5, 0), (-3, 5), (-8, 8)}
g⁻¹(5) = 0
h(x) = 3x - 10
h⁻¹(x) = (x+10)/3
h⁻¹(5) = 15/3 = 5
h(h⁻¹(5)) = 3(5) - 10
h(h⁻¹(5)) = 5
Thus, the value of g⁻¹(5) = 0, h⁻¹(x) = (x+10)/3, and the value of h(h⁻¹(5)) = 5 if g = {(-4, 1), (0, 5), (5, -3), (8, -8)} and h(x) = 3x - 10
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v = u + 2at
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and t is the time (in seconds).
Find v when u is 19 m/s, a is 3 m/s², and is 21 seconds.
Answer:
145 m/s
Step-by-step explanation:
v = u + 2at
v = 19 + 2(3)(21)
v = 19 + 126
v = 145
answer
V=145
Step-by-step explanation:
V=U+2at
v=19+2×3×21
v=19+126
v=145
Select the correct answer. Function f is an exponential function that is negative on the interval (-∞, 1) and positive on the interval (1, ∞). Which could be the graph of function f? A. An exponential function passes through (0, minus 6), (0.5, minus 2), (1, 0), (2, 2), (5, 3) B. An exponential function passes through (minus 1, minus 2), (minus 0.5, 0), (0, 1), and (4, 3) C. An exponential function passes through (minus 5, 3), (minus 2, 2), (minus 1, 0), and (0, minus 6) D. An exponential function passes through (minus 4, 3), (minus 1, 3.8), and (0, 5)
The exponential function which passes through (0,-2),(1,0),(2,2) (5,3) is negative on the interval (-∞,1) and positive on the interval (1,∞).
Given Function f is negative on the interval (-∞,1) and positive on the interval (1,∞)
We have to find the statement for which the exponential function' s values are given.
First option is having the statement which says that exponential
function passes through points (0,-6)(0.5,-2),(1,0),(2,2) (5,3). These points are showing the domain and value of the function which is codomain.
for x=0 it has -6,
for x=1 it has 0,
for x=2 it has 2,
for x=5 it has 3.
for x=0.5 it has -2
The description says that value of function is negative in interval (-∞,1) and positive in (1,∞) which is true for option A as it has negative values of -2 for x=0 and for x=2,5 it has value of 2 and 3.
Hence the function f is an exponential function passes through (0, minus 6), (0.5, minus 2), (1, 0), (2, 2), (5, 3).
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I’m having some problems understanding. I get it but don’t at the same time.
Answer:
C is the correct answer.
Step-by-step explanation:
-Angle 1 is not equal to Angle 5.
-Angle 3 + Angle 5 will not equal 180 degrees, since they are corresponding angles, not supplementary angles.
Though, Angle 8 is equal to Angle 6, likewise that 7 is equal to 9. Therefore, these angles will create a 180 degrees angle. This is because if 8 and 9 are supplementary, and 7 is a corresponding angle of 9, this will make Angle 8 + Angle 7 = 180 degrees.
In a survey of 4096 adults, 733 oppose allowing transgender students to use the bathrooms of the opposite biological sex Construct a 99% confidence interval for the population proportionInterpret the results A 99% confidence interval for the population proportion is (Round to three decimal places as needed)
A 99% confidence interval for the population proportion is; CI = (0.164, 0.194)
How to construct the confidence Interval?We are given;
Sample size; n = 4096
Number that opposed transgender students; x = 733
Thus;
Proportion; p^ = x/n = 733/4096 = 0.179
Formula for confidence interval of proportions is;
CI = p^ ± z√[p^(1 - p^)/n]
The z-value for confidence level of 99% is z = 2.576
Thus;
CI = 0.179 ± 2.576√[0.179(1 - 0.179)/4096]
CI = 0.179 ± 0.015
CI = (0.164, 0.194)
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Problem
Circles [tex]K[/tex] and [tex]L[/tex] touch externally at point [tex]P[/tex]. Line [tex]ABC[/tex] cuts [tex]K[/tex] at points [tex]A[/tex] and [tex]B[/tex] and is tangent to [tex]L[/tex] at [tex]C[/tex]. The line through [tex]A[/tex] and [tex]P[/tex] meets [tex]L[/tex] at a second point [tex]D[/tex].
Prove that [tex]PC[/tex] bisects angle [tex]BPD[/tex].
Step-by-step explanation:
Using the various theorems relating inscribed and external angles to intercepted arcs, we can write the following relations:
angle A = 1/2(arc BP) . . . . . . . . . . . inscribed angle
angle A = 1/2(arc CD -arc CP) . . . external angle at tangent/secant
angle CPD = 1/2(arc CD) . . . . . . . inscribed angle
angle CPB = 1/2(arc CP) + 1/2(arc BP) . . . . . sum of angles at the mutual tangent
ProofEquating the expressions for angle A, we have ...
1/2(arc BP) = 1/2(arc CD -arc CP)
Adding arc CP gives ...
1/2(arc BP +arc CP) = 1/2(arc CD)
Substituting the last two equations for angles from above, this gives ...
angle CPB = angle CPD
Hence PC bisects angle BPD.
Which of these triangle pairs can be mapped to each other using a reflection and a translation? a Triangles L R K and A R Q are connected at point R. Triangle L R K is reflected across point R to form triangle A R Q. b Triangles L P K and Q R A are shown. Triangle L P K is reflected across a line to form triangle Q R A. Triangle Q R A is shifted to the right of triangle L P K. c Triangles L P K and Q R A are shown. Triangle L P K is shifted down and to the left to form triangle Q R A. d Triangles L P K and Q R A are shown. Triangle L P K is rotated to form triangle Q R A. Triangle Q R A is also shifted to the right.
The triangle pairs that can be mapped to each other using a reflection and a translation is; Option B
How to Interpret Triangle Transformations?Let us analyze each of the graphs;
Option A; This graph didn't use a reflection and a translation because we see that there was first a reflection across side QR and then another reflection across side AR.
Option B; This graph is correct as it made use of a reflection and a translation as seen in the attached graph.
Option C; This didn't use of a reflection and a translation because it instead carried out translation both in vertical and horizontal direction.
Option D; This carried out Translation and Rotation.
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A swimming pool is 3 meters deep, 50 meters long, and 25 meters wide. If it takes 0.25 pounds of chlorine for every 15 cubic meters of water to keep the pool clean and healthy, how many pounds of chlorine are needed?
a. 27.2 pounds
b. 35.7 pounds
c. 45.4 pounds
d. 62.5 pounds
Answer:
D) 62.5 pounds.
Step-by-step explanation:
The volume of the swimming pool = [tex]3\times50\times25 =3750[/tex]
[tex]3750\div15 = 250[/tex] lots of 15
[tex]250\times0.25=62.5[/tex] pounds of chlorine.
Hope this helps, have a nice day!
Are the grades shown in the math class below normally distributed? Explain your answer.
Since the histogram is not symmetric, the grades shown in the math class below are not normally distributed.
When does a histogram represent a normal distribution?A histogram represents a normal distribution if it symmetric.
In this problem, we have that:
57% of the grades are on the left tail.25% of the grades are on the center.18% are on the right tail.Since the percentages at the tails are different, the histogram is not symmetric, and the grades shown in the math class below are not normally distributed.
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Translate this sentence into an equation.
22 more than Helena's score is 41.
Use the variable h to represent Helena's score.
Please help!!! What is the product to the following?
The product of 3x² and 2x³y + 5xy⁴ is given by the expression 6x⁵y + 15x³y⁴
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The product of 3x² and 2x³y + 5xy⁴ is:
= 3x² * (2x³y + 5xy⁴)
= 6x⁵y + 15x³y⁴
The product of 3x² and 2x³y + 5xy⁴ is given by the expression 6x⁵y + 15x³y⁴
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what are the values Of p and q ?
The values of p and q in the function f(x) = 2x³ + 17x² - 3px - 5q is p = 8, q = 27
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
x - 3 (i.e. x = 3) and x + 9 (i.e. x = -9) are factors of f(x) = 2x³ + 17x² - 3px - 5q
Hence:
f(3) = 0
2(3)³ + 17(3)² - 3p(3) - 5q = 0 (1)
Also:
2(-9)³ + 17(-9)² - 3p(-9) - 5q = 0 (2)
Hence, p = 8, q = 27
The values of p and q in the function f(x) = 2x³ + 17x² - 3px - 5q is p = 8, q = 27
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A patient is being given 2 1/3 milligrams of a drug per hour. How many total milligrams of the drug
will he get in 4 hours?
Answer:
it mean that the patient get 7mg drug in1 hour and infour hours he get 4×7= 28mg drug
State the restrictions of 1-x-y/x+y
The restriction of the expression as given in the task content is; x +y = 0.
What is the restriction of the expression?The expression in the task content is rational;
(1-x-y)/(x+y).
On this note, the restriction to the expression is the values which render the denominator of the expression equal to 0 and consequently the expression value to undefined.
Hence, the restriction is; x+y = 0.
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The vertex of this parabola is at (3,-2). When the x-value is 4, the
y-value is 3. What is the coefficient of the squared expression in the
parabola's equation?
O
O
A-1
B. 7
C. 1
D. 5
Answer:
5
Step-by-step explanation:
f(x) = a(x-3)² - 2
When x = 4, y = 3, so:
3 = a(4-3)² - 2
5 = a
QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer: 154 m^3
Step-by-step explanation:
Volume = (5*2*7) + (3*7*4)
= 70 + 84
= 154 m^3
Brainliest please :P
Answer:
154 m^3
Step-by-step explanation:
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The difference between two numbers is 120. If the smaller number is 720 what is the larger number?
Could someone help me out with this question?
The simplified form of the difference quotient of equation [tex]9x^2+5x-1[/tex] . in the form 9x + 9h + 5.
In question for equation [tex]9x^2+5x-1[/tex], simplified to difference quotient in the form of Ax+Bh+C where A, B, C are integers
equation is the relationship between variable and represented as [tex]9x^2+5x-1[/tex] is example of polynomial equation.
We know that,
for difference quotient
[tex]=\frac{f(x+h)-f(x)}{h} \\\frac{9(x+h)^2+5(x+h)-1-9x^2-5x+1}{h}\\\frac{9h^2+9hx+5h}{h}\\9x+9h+5[/tex]
While, compared with Ax+Bh+C
we have A=9, B=9, C=5.
Thus, The required value of difference Quotient in the form Ax+Bh+c where A, B and C is 9, 9 and 5 respectively
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To collect data from a number of people in a sample, use a/an ___________________. A. questionnaire B. group chart C. question log D. long form
To collect data from a number of people in a sample, use a questionnaire
What are questionnaires?Questionnaires are quantitative method used in research for information collection purpose.
This questionnaires consists of several question necessary to provide answers and solution to research questions and for the purpose of analysis. These questions can be open or closed ended questions depending on the nature of research.
Hence we can conclude that. to collect data from a number of people in a sample, use a questionnaire
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Eliminate the parameter in the equations x = 5cos(t) – 7 and y = 5sin(t) 9. how can the rectangular equation be described?
Recall that for all t,
cos²(t) + sin²(t) = 1
Now,
x = 5 cos(t) - 7 ⇒ (x + 7)/5 = cos(t)
y = 5 sin(t) + 9 ⇒ (y - 9)/5 = sin(t)
so that substituting into the identity above, we get
((x + 7)/5)² + ((y - 9)/5)² = 1
which we can rewrite as
(x + 7)²/25 + (y - 9)²/25 = 1
(x + 7)² + (y - 9)² = 25
and this is the equation of a circle centered at (-7, 9) with radius 5.
The difference between twice a number, x, and a smaller number, y, is 3. The sum of twice the number and the smaller
number is -3. Which equations represent this situation?
Oy=2x-3 and y=-2x-3
Oy-2x-3 and y=-2-2
O y=2x+3 and y=-2x-3
Oy-2x+3 and y=-x-
3. Help meeee
Answer:
y=2x+3 and y=-2x-3
Step-by-step explanation:
First situation:
2x-y=3
making y subject
y=2x+3
Second situation:
2x+y=-3
making y subject
y=-2x-3
The probability distribution for a
random variable x is given in the table.
X
-5 -3 -2 0 2
Probability .17 .13
3
133 16 .11 .10
Find the probability that -2 ≤x≤2
Considering the distribution given in the table, the desired probability is:
[tex]P(-2 \leq X \leq 2) = 0.6[/tex]
What is the probability distribution given in the table?The distribution is:
P(X = -5) = 0.17.P(X = -3) = 0.13.P(X = -2) = 0.33.P(X = 0) = 0.16.P(X = 2) = 0.11.P(X = 3) = 0.10.The values between -2 and 2(inclusive) are -2, 0 and 2, hence the desired probability is:
[tex]P(-2 \leq X \leq 2) = P(X = -2) + P(X = 0) + P(X = 2) = 0.33 + 0.16 + 0.11 = 0.6[/tex]
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Beginning inventory, purchases, and sales for WCS12 are as follows:
Oct. 1 Inventory 300 units at $12
13 Sale 190 units
22 Purchase 390 units at $15
29 Sale 300 units
a. Assuming a perpetual inventory system and using the weighted average method, determine the weighted average unit cost after the October 22 purchase. Round your answer to two decimal places.
The weighted average unit cost after the October 22 purchase is $13.70.
What is the weighted average unit cost?The weighted average unit cost determines the weighted average cost of all the purchased inventory.
[(300 x 12) + (390 x 15) ] / (300 + 390)
(3600 + 5850) / 690 = $13.70
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Can i get an answer ASAP
A rectangle has perimeter 92 cm and its length is 1 cm more than twice its width.
Find the dimensions of a rectangle given that its perimeter is 92 cm and its length is 1 cm more than twice its width.
Set up your solution using the variables L for the length, W for the width, and P for the perimeter.
Part a: Using the definition of perimeter, write an equation for P in terms of L and W .
Part b: Using the relationship given in the problem statement, write an equation for L in terms of W .
Solve the equations from parts a and b.
Part c: The width is
Number
cm.
Part d: The length is
Number
cm.
The length and width of the rectangle is 15cm and 31cm respectively
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
where
L is the length
W is the width
If its length is 1 cm more than twice its width, then;
L = 2W + 1
Substitute
92 = 2(2W + 1 + W)
46 = 3W + 1
3W = 45
W = 15cm
Determine the length
L = 2(15) + 1
L = 31cm
Hence the length and width of the rectangle is 15cm and 31cm respectively
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Search the internet regarding Golden Ratio explain its history significance and find its value in fraction/decimal give at least five examples from nature surroundings human body architecture etc manifesting the concept of Golden ratio please write in easy words for grade 4
help please
Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
What is the Golden ratio?It should be noted that the Golden ratio is also called the golden mean or divine proportion.
The Golden ratio is refered to as the. most beautiful number in the universe.
It is extraordinary because it can be visualized everywhere from geometry to the human body.
In this case, quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
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