Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)
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Explanation Section:
It is false
If f(x) is a function , then for each value of x there should be a single y values
For input 0 there is a output 0
for input 10, the output is 2
for input 15, output is 3
For input 5, we have two output 1 and 3
for single input 5, the function cannot have two outputs 1 and 3
So this f(x) is not a function
Bye! - SunnyBunny <3
I need help with this math question.
Answer:
23 children and 9 adults
p <= 70/9
Step-by-step explanation:
Let x = # of adults and y = # of children. The number of children is 5 more than twice the number of adults, so x = 2y + 5. The total cost of entrance is $6525, so 225x + 150y = 6525.
x = 2y + 5
225x + 150y = 6525
x - 2y = 5
225x + 150y = 6525
75x - 150y = 375
225x + 150y = 6525
300x = 6900
x = 23
x = 2y + 5
23 = 2y + 5
18 = 2y
y = 9
225p + 3750 <= 5500
225p <= 1750
p <= 70/9
1.Name 4 other angles whose cosine is the same as cos pi/3 . Explain using mathematical language how you know this is true.
2.Is this statement true or false? Explain your answer.
All angles that have the same cosine will have the same sine.
The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3
How to illustrate the information?From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.
Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.
Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.
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True or false? the patient should be given a receipt for payments on account even if the account is not paid in full.
Answer:
Step-by-step explanation:
true
Answer:
False because the account isn't full
the angle of depression from the top of the tower to a boulder on the ground is 38 degrees if the tower is 25 m high how far from the base of the tower is the boulder
Check the picture below.
Make sure your calculator is in Degree mode.
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 x 4 x g(x) –2 1 –1 3 0 5 1 7 2 9 (-2, 10) (–1, 7) (0, 5) (1, 7)
The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:
g(x) = 5 + 2x.
The solution to the system of equations is found as follows:
f(x) = g(x)
2x² + x + 4 = 5 + 2x
2x² - x - 1 = 0
Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(2)(-1) = 9[/tex][tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{9}}{4} = 1[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{9}}{4} = -0.5[/tex]When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).
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Answer:
D. (1,7)
Step-by-step explanation:
I took the exam
find the perimeter and area of the polygons
Answer:
Below in bold.
Step-by-step explanation:
This figure is a trapezoid.
We can find the missing side length by applying the Pythagoras Theorem to the right triangle on the left of the figure.
The dotted line has length 12 cm and the base of the triangle = 25 - 18 = 7 cm
So x^2 = 12^2 + 7^2 (where x = missing length)
= 144 + 49
= 189
x = √189
= 13.75 to nearest hundredth
So the perimeter
= 18 + 12 + 25 + 13.75
= 68.75 cm.
Area of a trapezoid = 1/2 (a + b) * h.
Area = 1/2 *(18 + 25) * 12
= 258 cm^2.
A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.
garden bordered by a river
What dimensions would guarantee that the garden has the greatest possible area?
shorter side: _____ft (feet)
longer side: ____ft (feet)
greatest possible area: ___ft2 (square-feet)
The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
What dimensions would guarantee that the garden has the greatest possible area?The given parameter is
Perimeter, P = 520 feet
Represent the shorter side with x and the longer side with y
One side of the garden is bordered by a river:
So the perimeter is:
P = 2x + y
Substitute P = 520
2x + y = 520
Make y the subject
y = 520 - 2x
The area is
A = xy
Substitute y = 520 - 2x in A = xy
A = x(520 - 2x)
Expand
A = 520x - 2x^2
Differentiate
A' = 520 - 4x
Set to 0
520 - 4x = 0
Rewrite as:
4x= 520
Divide by 4
x= 130
Substitute x= 130 in y = 520 - 2x
y = 520 - 2 *130
Evaluate
y = 260
The area is then calculated as:
A = xy
This gives
A = 130 * 260
Evaluate
A = 33800
Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
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Use the figure to the right to list all of the pairs of angles that fit each description.
The pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Angle DescriptionFrom the question, we are to list the angles that fit the given descriptions
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W;
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Hence, the pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
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determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.
A. none of these
B. quadratic
C. linear
D. exponential
The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.
According to the statement
we have given that:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
And we have to find that The type of model that best fits the given situation.
So, according to the linear representation model
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
y = mx + c
And Slope of a function is
m = y₂ - y₁ / x₂ - x₁
Then
m = 5500 - 5000 / 19 - 20
m = -500
So, the equation become
y = -500x +c
And find the value of by putting the values.
So, c = 15000
And the equation become
y = -500x + 15000.
According to this linear model is perfect for this situation.
So, The linear representation model is best for this situation.
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What is the exact value of cos (67.5°)?
OA.
OB.
OC. -√2+√2
√2+√2
2
-
√2-√2
2
OD. √2+ √2
4
first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so
[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]
The student’s t distribution will approach the standard normal distribution as the number of the degrees of freedom goes up.
a. True
b. False
Answer:
True student distribution will approach the standard
Using data from a study, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data from this study.1 In this case, we are testing
H0:po=pcHa:po>pc
where po and pc represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have n1=n2=500. Show all remaining details in the test, using a 5% significance level.
Effect of Organic Raisins After 15 Days
After 15 days, 320 of the 500 fruit flies eating organic raisins are still alive, while 300 of the 500 eating conventional raisins are still alive.
Give the test statistic and the p-value.
Round your answers to three decimal places.
What is the conclusion?
Do we have evidence that the proportion surviving after eating organic is higher?
The hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.
How to illustrate the information?The following can be deduced from the information:
x1 = 275
x2 = 170
n1 = 500
n2 = 500
The sample proportion will be:
p1 = 275/500 = 0.55
p2 = 170/500 = 0.34
The pooled proportion will be:
= (275 + 170)/(500 + 500)
= 0.44
The test statistic is 6.681. It should be noted that the test statistics is a number that's calculated by a statistical test. It shows how the observed data are far from the null hypothesis.
The p value in this scenario is extremely small. The p value is a measurement used to validate a hypothesis against the observed data. Therefore, we have to reject the null hypothesis.
In this case, the hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.
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help please!! show work if possible thank you!!
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]F = \frac{S + 24}{3}[/tex]
Step-by-step explanation:
We know that:
[tex]S = 3F -24[/tex],
where F is the length of the foot of a person, and S is their shoe size.
To solve for the length of a person's foot, we have to rearrange the given equation to make F the subject:
[tex]S = 3F -24[/tex]
⇒ [tex]S + 24 = 3F[/tex] [adding 24 to both sides]
⇒ [tex]\frac{S + 24}{3} = F[/tex] [dividing both sides by3]
⇒ [tex]F = \frac{S + 24}{3}[/tex] [swapping the sides]
How did doves view the conflict in Vietnam?
O As a vital Cold War battleground in the fight for democracy
O As a localized civil war that should not include the US
O As the first step in acquiring territory in Southeast Asia
O As a means to achieving Johnson's Great Society
The view of war doves with respect to the Vietnam War was that: B. as a localized civil war that should not include the United States of America (US).
What is the Vietnam War?The Vietnam War is also referred to as Second Indochina War or the Vietnam conflict and it can be defined as a short, costly, protracted and divisive conflict between the communist government of North Vietnam and South Vietnam, which ended on the 30th of April, 1975.
Based on historical information and records, the Vietnam War officially started on the 1st of November, 1955 in the following locations:
VietnamCambodiaNorth VietnamSouth VietnamLaosSouth East AsiaIn conclusion, we can infer and logically deduce that the view of war doves with respect to the Vietnam War was that it is a a localized civil war and as such should not include the United States of America.
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Using f(x), what is the equation that represents g(x)?
Og(x) = log5 (x) - 3
O
g(x) = log5 (x) +3
Og(x) = log5 (x-3)
Og(x) = logs(x + 3)
The equation that represents the function g(x) is g(x) = log₅(x - 3)
How to determine the equation that represents g(x)?The equation of the function f(x) is given as:
f(x) = log₅(x)
From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)
This means that
g(x) = f(x - 3)
The function f(x - 3) is calculated as follows
f(x - 3) = log₅(x - 3)
Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)
g(x) = log₅(x - 3)
Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)
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For the same sample data and null hypothesis, how does the p-value for a two-tailed test of μ compare to that for a one-tailed test?.
A one-tailed test's p-value is half that of a two-tailed test.
What is the difference between the p-value for a two-tailed test and a one-tailed test?Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.
What is null hypothesis ?Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.
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please help 20 points and brainlyist
a) 1. The backpack weight sample mean is 6.375 pounds.
a) 2. The backpack weight sample mean is 6.375 pounds.
a) 3. The backpack weight sample mean is 6.625 pounds.
b) The range of the sample means is between 6.375 and 6.625, which approaches 0.250 pounds, plus or minus.
c) Since the students are using the sample means to estimate the mean backpack weight of their schoolmates, the true statements are A. and D.
The farther the range of the sample means is from O, the less confident they can be in their estimate.
What is a sample mean?A sample mean is a statistic computed from a sample of data or variables.
The sample mean represents the average value of the sample data.
What is a range in statistics?The range describes the difference between the largest number and the smallest number.
Thus, based on the range of the sample means, the farther it is from 0, the less confident the students can be in their estimate.
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Round each fraction to help you estimate the solution for the following equation:
nine tenths minus eight tenths equals
0
one half
1
one and one half
Answer:
Step-by-step explanation:
answer is 1/2
Which of the following inequalities is graphed on the coordinate plane? A. y>-2x+1 B. y>-2x+1 C. y<-2x+1 D. y<-2x+1
The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Answer: The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?
The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Step-by-step explanation:
Find the term that must be added to the equation x2 6x=1 to make it into a perfect square.
The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].
What is a perfect square?
A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.
The perfect square trinomial exists
[tex](a[/tex] ± [tex]b)^2[/tex] = [tex]a ^2[/tex] ± 2ab + [tex]b ^2[/tex]
[tex]$x^2-6x=1[/tex]
[tex]x^2-2*3x=1[/tex]
then [tex]$2ab = 2 * 3*x = 2 * x *3[/tex]
The value of a = x and b = 3
[tex]$b^2=3^2=9[/tex]
[tex]$x^2-6x+9=1+9[/tex]
[tex]$x^2-6x+9=10[/tex]
The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].
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find the maximum value of c=4x+2y subject to the fallowing constraints x≥0 y≥0 2x+2y≤10 3x+y≤9
The maximum value of c=4x+2y subject to the constraints is 14
How to determine the maximum value?The objective function is given as:
c = 4x+2y
The constraints are given as:
x≥0 y≥0
2x+2y≤10
3x+y≤9
Rewrite 2x+2y≤10 and 3x+y≤9 as equations
2x+2y = 10
3x+y = 9
Divide 2x+2y = 10 through by 2
x+y = 5
Subtract x+y = 5 from 3x+y = 9
3x - x + y - y = 9 - 5
Evaluate the difference
2x = 4
Divide by 2
x = 2
Substitute x = 2 in x+y = 5
2+y = 5
Solve for y
y = 3
So, we have
(x, y) = (2, 3)
Substitute (x, y) = (2, 3) in c = 4x+2y
c = 4 * 2 + 2 * 3
Evaluate
c = 14
Hence, the maximum value of c=4x+2y subject to the constraints is 14
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Find the missing side. Round your answer to the nearest tenth.
What are the steps to finding missing sides
Answer:
23.6
Step-by-step explanation:
→ Identify length not given
Opposite
→ Find a formula without opposite
Cos = Adjacent ÷ Hypotenuse
→ Rearrange
Adjacent = Cos × Hypotenuse
→ Substitute
cos 38 × 30 = 23.6
Answer:
[tex]x = 23.6[/tex]
Step-by-step explanation:
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is [tex]x[/tex] (required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].
Substituting into the formula:
[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]
⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]
⇒ [tex]x = 23.6[/tex]
Instead of recording the number 1.23 cm for the radius of 2 tube, a student recorded 1.32cm.find the percentage error, correct to 1.DP
In a local shop some items are being sold at a third off. They now cost the following amounts. What was the original full price? 40 POINTS AND BRAINLIEST
1.£6.46
2.£58.24
3.£114.28
4.£12.50
5.£10.86
Answer:
1) 9.69
2) 87.36
3) 171.42
4) 18.75
5) 16.29
Step-by-step explanation:
Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5
Answers are needed urgently..ty
Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.
The length of the straight line AB = 80cm
Calculation of angle of a triangleThe angle at a point = 360°
Angle AQB= 360 - 210° = 150
But the angle that makes up a triangle= 180°
180-150= 30°
But <QAB = <QBA because triangle AQB is an isosceles triangle.
30/2 = 15°
To calculate the length of the straight line the following is carried out using the sine laws.
a/ sina, = b sinb
a= 8cm, sin a { sin 15)
b= ? , sin B = 150
make b the subject formula;
8/sin15= b/sin 150
b= 8 × sin 150/sin 15
b= 80cm
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A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees.
What is the measure of Arc A U?
44°
50°
64°
92°
The measure of Arc AU of the given Circle Geometry is; 50°
How to find the measure of arc angle?The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”
We can express the above theorem as;
Angle at the center = 2 × Angle at the circumference
From the attached image below and from the given statement in the question, we are given that; ∠QUA = 111°
Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA
m∠QDA = 2 × 111° = 222°
Which gives;
∠QOA = = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA (by angle addition property)
Thus;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
Thus, the measure of Arc AU is;
Arc AU = ∠UOA = 50°
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Answer: b
Step-by-step explanation:
The area of a square is 400 square units. If the length of each side of the
square increased by one unit, would its area be a rational number? Explain.
yes it will be a rational number.
square having area 400 sq units will have a length of 20 on each side by increasing the length of each side by 1 we get 21 then the area will be
21 ^ 2=441
Then we will have a rational number.
I don't get the minutes part
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is: $20,000 loan from a partner. $30,000 of profits from the last year of operations. $3,000 payable to a supplier. $100,000 in capital balances of the partners.
The correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations. What is the uniform partnership act?The Uniform Partnership Act (UPA) governs corporate partnerships in various states in the United States. When a partner dissociates, the UPA provides regulations for the dissolution of the partnership. Several revisions to the Uniform Partnership Act have been made over the years (UPA). The Revised Uniform Partnership Act refers to the revised act and changes (RUPA).The Uniform Partnership Act also governs partnership formation, liabilities, assets, and fiduciary obligations.Marshaling of assets:
The process of organizing the balance sheet elements (assets and liabilities) in a specified sequence is referred to as the marshaling of assets and liabilities. In other words, it is the process of organizing the various assets and liabilities on a balance sheet in a particular order.The order is the amount owed to a supplier, the amount of a loan from a partner, the amount of the partners' capital balances, and the number of profits from the previous year of operations.Therefore, the correct order is 3,1,4,2.
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The correct question is given below:
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is:
(1) $20,000 loan from a partner.
(2) $30,000 of profits from the last year of operations.
(3) $3,000 payable to a supplier.
(4) $100,000 in capital balances of the partners.
