The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8)
How to estimate proportion?The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8).
When we are talking about population parameters, we also have to look at the way of estimating the population, we have to add two extremes and divide by 2.
Thus, the correct one is;
(0.5 + 0.8)/2 = 0.65
Read more about Population parameter at; https://brainly.com/question/2292917
#SPJ1
( brain + 95 points ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.
Area of base
1/2BH1/2(4)(6)2(6)12cm²Volume
Area of base× height12(10)120cm³A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
The function f(x) = x + 21 is one-to-one.
a. Find an equation for f1(x), the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¯¹ (f(x)) = x.
Answer:
a. D. f⁻¹(x) = x - 21, for all x
b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x
Step-by-step explanation:
See attached picture.
The required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:
x = y + 21
Now, let's solve for y:
y = x - 21
Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.
b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.
First, let's calculate f(f(x)):
f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42
Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.
Now, let's calculate f¯¹(f(x)):
f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x
Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.
Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Therefore, the required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Learn more about inverse functions here:
https://brainly.com/question/29141206
#SPJ2
Seven increased by the product of six and the number is 19
The number is that was multiplied by 6 is 2.
What is the number?The equation that can be derived from the question is :
7 + (6a) = 19
Where a is the unknown number that 6 was multiplied with
Given the above equation, in order to determine the value of a, take the following steps:
Combine similar terms: 6a = 19 - 7
Subtract similar terms: 6a = 12
Divide both sides by 6: a = 12 / 6
a = 2
Here is the complete question:
Seven increased by the product of six and the number is 19. What is the number?
To learn more about division, please check: https://brainly.com/question/194007
#SPJ1
X =
(19) Find the values for X and Y, and then solve for the side lengths.
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
Which of the following is an arithmetic sequence with common difference –5?
The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...
What is the Common Difference of an Arithmetic Sequence?The common difference of an arithmetic sequence is determined as: a term - previous term.
For the sequence, 8, 3, -2, -7,.. the common difference is:
-7 - 2 = -2 - 3 = 3 - 8 = -5.
Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...
Learn more about common difference on:
https://brainly.com/question/503167
#SPJ1
Which of the following is an even function?
Of(x) = (x - 1)²
Of(x) = 8x
Of(x)=x²-x
Of(x) = 7
COFFE
Sinte echinat
SUMPARNI
Answer:
Step-by-step explanation:
Can someone help me with this math problem?
see attached photo
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
How to determine the value of trigonometric reasons
In this question we must take into accounts the definitions of the trigonometric reasons sine and secant and the Pythagorean theorem as well.
If sec θ < 0 and csc θ > 0, then sin θ > 0 and cos θ < 0, the angle is in the second quadrant (0.5π < θ < π, x < 0, y > 0) and we have the following expression:
sec θ = r/x
[tex]\frac{r}{x}= -\frac{6\sqrt{11}}{11}[/tex]
Then x = - 11, r = 6√11 and the value of y is:
[tex]y = \sqrt{r^{2}-x^{2}}[/tex]
y = 5√11
By trigonometric expressions we have this formula for sin 2θ:
sin 2θ = 2 · sin θ · cos θ
sin 2θ = 2 · (y/r) · (x/r) = (2 · x · y)/r²
sin 2θ = [2 · (- 11) · (5√11)]/396
sin 2θ = - (5/18) · √11
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
To learn more on trigonometric reasons: https://brainly.com/question/6904750
#SPJ1
a group of 20 students in four adults are going on a field trip to the museum What is the ratio of students to adults complete the statement.
Answer:
5:1
Step-by-step explanation:
Originally the ratio is 20:4
but then it is simplified to 10:2
then 5:1
Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers
Answer:
Numbers are 5 , 7
Step-by-step explanation:
Forming quadratic equation and solving:Let the two consecutive odd numbers be (2x + 1) and (2x + 3)
Their product = 35
(2x + 1)(2x + 3) = 35
Use FOIL method.
2x*2x + 2x*3 + 1*2x + 1*3 = 35
4x² + 6x + 2x + 3 = 35
Combine like terms
4x² + 8x + 3 = 35
4x² + 8x + 3 - 35 = 0
4x² + 8x - 32 = 0
Quadratic equation: 4x² + 8x - 32 = 0Solving:
4x² + 8x - 32 = 0
Divide the entire equation by 2
[tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]
2x² + 4x - 16 = 0
Sum = 4
Product = -32
Factors = 8 , (-4)
When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.
Rewrite the middle term
2x² + 8x - 4x - 16 = 0
2x(x + 4) - 4(x + 4) = 0
(x + 4) (2x - 4) = 0
2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}
2x = 4
x = 4/2
x= 2
2x + 1 = 2*2 + 1 = 5
2x + 3 = 2*2 +3 = 7
The numbers are 5 , 7
ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?
Answer:
? = 41.41°
Step-by-step explanation:
The known side length is adjacent to the angle we need to find hence we will use cosine
cosx = adjacent /hypotenuse
cos(?) = 6 / 8
simplify fraction, cos(?) = 3 / 4
? = arccos(3 / 4)
y=-3³ +4
step by step of the rules and formula of this equation
find the perimeter of a triangular field whose length of edges are 14 m, 12m 10 m Also find the length of required to fence 4 times around it?
Answer: 36 m, 144 m
Step-by-Step Explanation:
a = 14 m
b = 12 m
c = 10 m
Perimeter = a + b + c
Therefore,
= a + b + c
= 14 + 12 + 10
= 26 + 10
=> 36
Perimeter = 36 m
Length of Fence required for Fencing 4 times = Perimeter * 4
Therefore,
= Perimeter * 4
= 36 * 4
= 144
Length of Fence required for Fencing 4 times = 144 m
Sin 0 = -8/17 and cos 0 = 15/17 find tan0
Answer:
Step-by-step explanation:
Givens
sin(theta) = - 8/17
cos(theta)= 15/17
Tan(theta) = ?
Comment
Without using the Pythagorean Theorem, you could simply use tan(theta) = Sin(theta) / cos(theta)
Tan(theta) = sin(theta) / cos(theta)
Tan(theta) =[tex]\dfrac{\dfrac{-8}{17} }{\dfrac{15}{17} }[/tex]
Now turn the bottom fraction upside down and multiply.
Tan(theta) = [tex]\dfrac{-8}{17}*\dfrac{17}{15} = \dfrac{-8}{15}[/tex]
Answer Tan(theta) = -8/15
The grade 10 class is going to bake muffins. The recipe that they are going to use requires the following ingredients: RECIPE ✓2 Egga ✔125ml Cooking oll ✓375ml brown sugar (300g) ✓800ml Milk ✓300g Whole wheat flour ✓ 375ml cake flour (210g) ✓5ml Salt ✓ 5ml Vanilla Essence ✓ 10ml Bicarbonate of soda ✓ 250ml Raisins (150g) 2.1 The volume of 150g of Whole wheat is 250ml. Calculate the volume of the Whole wheat flour in the recipe 2.2 When they are all mixed together, all the above ingredients make up 2 litres of mixture (because some parts dissolve into other parts). 2.2.1 Convert 2 litres into ml 2.2.2 How many muffins can the above recipe make if 60ml is required for each muffin? 2.2.3 Using your answer to question 2.2.2, how many eggs will the girls need to buy to make 500 muffins? 2.3 The students need to make 500 muffins, using muffin trays that hold 6 muffins par tray. They plan to put 4 trays at a time into the ovens. Each oven takes 30 minutes to bake. How long will they take to make 500 muffins if they will be using 4 ovens?
The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.
How to convert?From the information, we are told to convert 2 litres into ml. This will be:
= 1000 × 2
= 2000ml
The number of eggs that will be bought to make 500 muffins will be:
= 500 × 2
= 1000 eggs.
Learn more about conversion on:
brainly.com/question/97386
#SPJ1
7) $72.45 -28.98 Rounded estimate
Answer:
$43
Step-by-step explanation:
$72.45 can be rounded down to $72.00
$28.98 can be rounded up to $29.00
$72-$29= $43
can you help me with this question
Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
Consider the function.
Which conclusions can be drawn about f–1(x)? Select two options.
f–1(x) has a slope of .
f–1(x) has a restricted domain.
f–1(x) has a y-intercept of (0, –36).
f–1(x) has an x-intercept of (–36, 0).
f–1(x) has a range of all real numbers.
The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
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.
The question is incomplete.
The question is: Consider the function f(x) = (-2/3)x - 24 Which conclusions can be drawn about f⁻¹(x) Select two options:
f⁻¹(x) has a slope of -2/3
f⁻¹(x) has a restricted domain.
f⁻¹(x) has a y-intercept of (0, –36).
f⁻¹(x) has an x-intercept of (–36, 0).
f⁻¹(x) has a range of all real numbers.
f(x) = (-2/3)x - 24
To find the inverse of a function:
interchange the x and y
x = (-2/3)y - 24
y = (-3/2)(x + 24)
y = (-3/2)x - 36
The slope of a function f⁻¹(x) is -3/2
From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.
Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
Answer:
D and E
Step-by-step explanation:
did the test
Which function is shown in the graph below?
O y = logo 4x
O y = log₁x
O y = log3x
O y = log10x
The correct function shown in the graph is,
⇒ log₁₀ (ax) = 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:
⇒ log₁₀ (ax) = 1
or , ax = 10¹ = 10
Thus, x = 10/a
So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .
⇒ log (3 × 3.33) = 0.99 ≈ 1
Thus, out of the given options only Option D seems to be the most probable answer.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ5
HELP!!!!!!!!!!!!!!!!!!!!
Answer:
D is the answer hope
Step-by-step explanation:
hope this helped
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
the lenghts of five boxes are shown in the table which line plot shows the data from the table
Answer:
The bottom right line plot.
Step-by-step explanation:
In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.
Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
Solve for p: -3p + 2 > 5
To solve these types of problems:
⇒ just solve like a regular algebraic equation
⇒ with an inequality sign in the middle
Let's solve:
[tex]-3p + 2 > 5\\-3p > 3[/tex]
whenever there is any division/multiplication⇒ must change the inequality sign to face the other direction
[tex]-3p > 3\\p < -1[/tex]
Answer: p < -1
Hope that helps!
Answer:
p < -1
Step-by-step explanation:
-3p + 2 > 5
subtract 2 from both sides
-3p + 2 - 2 > 5 - 2
-3p > 3
divided both sides by -3 to get p alone
-3p / -3 > 3 / -3 reverse the inequality
p > -1
A rectangular deck has a length of 12 feet and a perimeter of 36 feet. What is the deck's width and area?
Answer:
Deck's width is 6 feet.The area is 72 sq. ft.Step-by-step explanation:
First, label it out:
Length: 12 ft.Width: ?Area: ?Perimeter: 36 ft.Then, we add up 12 twice (Since the length is on 2 sides):
12 + 12 = 2436 - 24 = 1212 - ? = ?Now, we write down a 6 in the ?:
12 - 6 = 6.Width = 6.
We are not done!
Now, we have to solve for area.
12 * 6= 72Answers are:Area = 72 sq. ft.Width = 6 ft.
If £2000 is placed into a bank account that pays 3% compound interest per year
how much will be in the account after 2 years?
Answer:
£ 2121.8
Step-by-step explanation:
The formula to find the compound interest is :
[tex]A=P(1+\frac{R}{100} )^n[/tex]
Here,
A = Amount ⇒ ?
P ⇒ Principal ⇒ £2000
R ⇒ Interest rate ⇒ 3%
n ⇒ Time ⇒ 2 years
Let us find now.
[tex]A=P(1+\frac{R}{100} )^n[/tex]
[tex]A=2000(1+\frac{3}{100} )^2[/tex]
[tex]A=2000(1+0.03 )^2[/tex]
[tex]A=2000(1.03 )^2[/tex]
[tex]A=2000*1.0609[/tex]
[tex]A=2121.8[/tex]
Therefore, there will be £ 2121.8 in the bank account after 2 years.
please help asap 100 points
Answers:
Problem #1: Option C, 166 yards cubed
Problem #2: Option A, 10
Step-by-step solution:
The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it. Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.
Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder. However, before doing that we need to determine the radius of the circle from the diameter that was given.
Divide the diameter by two to get the radius
[tex]Radius = \frac{Diameter}{2}[/tex][tex]Radius = \frac{5.2\ yd}{2}[/tex][tex]Radius = 2.6\ yd[/tex]Plug in the values
[tex]V_{cylinder} = (\pi * radius^2)*height[/tex][tex]V_{cylinder} = (\pi * (2.6\ yd)^2)*7.8\ yd[/tex]Simplify the exponent
[tex]V_{cylinder} = (\pi * (2.6)^2 *(yd)^2)*7.8\ yd[/tex][tex]V_{cylinder} = (\pi * 6.76\ yd^2)*7.8\ yd[/tex]Simplify the expression
[tex]V_{cylinder} = (21.237\ yd^2)*7.8\ yd[/tex][tex]V_{cylinder} = 165.65\ yd^3[/tex]Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.
Now that we completed the first question, we can move onto the second question. In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of. We need to use the Secant-Secant Power Theorem to help determine our solution.
Make an expression to represent the scenario
[tex]32(x + 32) = 28(20 + 28)[/tex]We know have an expression which we can now simplify and get the value of the unknown easily. The first step would be to distribute the 32 and 28.
Distribute both sides
[tex]32(x + 32) = 28(20 + 28)[/tex][tex](32 * x) + (32 * 32) = (28 * 20) + (28 * 28)[/tex][tex]32x + 1024 = 560 + 784[/tex]Simplify the expression
[tex]32x + 1024 = 1344[/tex]We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.
Subtract 1024 from both sides
[tex]32x + 1024 - 1024 = 1344 - 1024[/tex][tex]32x = 1344 - 1024[/tex][tex]32x = 320[/tex]The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.
Divide both sides by 32
[tex]\frac{32x}{32} = \frac{320}{32}[/tex][tex]x = \frac{320}{32}[/tex][tex]x = 10[/tex]After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.