The correct options are 2, 3, and 5 for the statements "The graph of the function is a parabola," "The graph contains the point (0, 0)," and "The graph of the function opens down" respectively.
What is the quadratic function?
A quadratic function is a type of polynomial function with a degree of 2, meaning it has the form:
[tex]f(x) = ax^2 + bx + c[/tex]
The correct statements are:
The value of f(-10) = 82: This statement is true because we can plug in -10 for x in the given quadratic function [tex]f(x) = x^2 - 5x + 12[/tex]and evaluate to get [tex]f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162[/tex], not 82.The graph of the function is a parabola: This statement is true because the given function [tex]f(x) = x^2 - 5x + 12[/tex]is a quadratic function, and the graph of a quadratic function is always a parabola.The graph contains the point (0, 0): This statement is false because when we plug in x = 0 into the given quadratic function [tex]f(x) = x^2 - 5x + 12[/tex], we get [tex]f(0) = 0^2 - 5(0) + 12 = 12[/tex], so the point (0, 0) is not on the graph of the function.The graph contains the point (20, -8): This statement is not mentioned in the given options, so we cannot determine its truthfulness based on the given information.The graph of the function opens down: This statement is false because the coefficient of [tex]x^2[/tex] in the given quadratic function f(x) = [tex]x^2 - 5x + 12[/tex] is positive (+1), which means the parabola opens upwards, not downwards.Hence, the correct options are 2, 3, and 5 for the statements "The graph of the function is a parabola," "The graph contains the point (0, 0)," and "The graph of the function opens down" respectively.
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A parallelogram has sides of length 19 units and 10 units. The shorter diagonal is 12 units. Find the measure of the longer diagonal. Round to 2 decimal places, if necessary.
The measure of the longer diagonal is approximately 26.01 units, rounded to two decimal places.
What is parallelogram?A parallelogram is a four-sided flat geometric shape, with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other, and the opposite angles are equal in measure. A parallelogram can also be thought of as a slanted rectangle, where the sides are not perpendicular to each other.
Let's denote the longer diagonal of the parallelogram as "d". We know that the diagonals of a parallelogram bisect each other, so the shorter diagonal, which is 12 units, divides the parallelogram into two congruent triangles. Let's use the Pythagorean theorem to find the height of one of these triangles:
a² + b² = c²
where a = half of the shorter diagonal = 12/2 = 6 units, b = height of the triangle, and c = half of the longer diagonal.
Substituting the given values, we have:
6² + b² = c²
36 + b² = c²
b² = c² - 36
Now, let's use the fact that the sides of a parallelogram are parallel and opposite in direction to write another equation:
c² = (19 + 10)²
c² = 729
Substituting this value into the previous equation, we have:
b² = 729 - 36
b² = 693
Taking the square root of both sides, we get:
b ≈ 26.33
Since the height of the parallelogram is perpendicular to the longer diagonal, we can see that the longer diagonal is the hypotenuse of a right triangle with legs of 10/2 = 5 units and 26.33 units. Using the Pythagorean theorem again, we can solve for the longer diagonal:
a² + b² = c²
where a = 5, b = 26.33, and c = the longer diagonal.
Substituting the given values, we have:
5² + 26.33² = c²
676.56 = c²
c ≈ 26.01
Therefore, the measure of the longer diagonal is approximately 26.01 units, rounded to two decimal places.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y² -5y = 750750 -y(y -5) = 0(y +25)(y -30) = 0Step-by-step explanation:
You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.
AreaThe area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...
A = LW
750 = y(y -5)
This equation can be rearranged into several different forms:
y² -5y = 750 . . . . . . . multiply it out
750 -y(y -5) = 0 . . . . . subtract the right side expression
(y +25)(y -30) = 0 . . . . factor it
41 Points!! Multiple choice algebra question. Use the value of the discriminant to determine the number and type of roots for the equation x^2-3x+7=0. Photo attached. Thank you!
Since the discriminant is negative, the equation has two complex conjugate roots is -19.
How to find complex conjugate roots?To find complex conjugate roots of a polynomial, you can follow these steps:
Identify the complex roots of the polynomial: Use the quadratic formula or any other method to find the roots of the polynomial. If the roots are complex, they will be of the form a + bi, where a and b are real numbers and i is the imaginary unit.
Check for conjugate pairs: If a complex root is of the form a + bi, then its complex conjugate will be a - bi. Check if the polynomial has any other root of the form a - bi. If so, then the two roots are complex conjugates.
For example, suppose you have a polynomial with the equation:
[tex]x^3 - 4x^2 + 7x - 10 = 0[/tex]
Using a calculator or other methods, you can find that one of the roots of this polynomial is approximately 1.72 + 0.98i. To check if this is part of a complex conjugate pair, you can check if the polynomial has another root of the form a - bi.
One way to do this is to use polynomial long division to divide the original polynomial by the quadratic factor (x - (1.72 + 0.98i)) (x - (1.72 - 0.98i)).
To determine the number and type of roots of the equation x^2 - 3x + 7 = 0, we need to use the discriminant, which is given by the formula b^2 - 4ac.
In this case, a = 1, b = -3, and c = 7. Substituting these values into the formula, we get:
[tex]b^2 - 4ac = (-3)^2 - 4(1)(7) = 9 - 28 = -19[/tex]
Since the discriminant is negative, the equation has two complex conjugate roots.
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Find three consecutive integers such that 4 times the first added to the third is 92
Solve quickly Thanks
The three consecutive integers are 18, 19, and 20.
What is consecutive integers?Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.
According to question:Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:
4x + (x+2) = 92
Simplifying this equation, we get:
5x + 2 = 92
Subtracting 2 from both sides, we get:
5x = 90
Dividing both sides by 5, we get:
x = 18
Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:
4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.
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In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%
Therefore , the solution of the given problem of percentage comes out to be D) 28% is the right response.
What is percentage?The shorthand "a%" is used in statistics to represent a number or metric that may be expressed as a percentage of 100. Additionally strange spelling include "pct," "pct," as "pc." The approach that is most frequently employed for this is the percentage symbol ("%"). Any hints or set proportions of any part for the total are also unknown. Since numbers commonly add up to 100, they are effectively integers.
Here,
According to the facts provided, 30% of the male population and 60% of the people in Math Town are male.
This suggests that between 30% and 60% of people have brown eyes.
Let's figure out what proportion of the entire population is equal to 30% of 60%:
=> 30% of 60% = (30/100) * (60/100)
=> 0.3 * 0.6
=> 0.18 or 18%
Therefore, brown eyes are present in Math Town's overall population of 18%.
Since the only other gender listed is females and we are aware that 18% of the population as a whole has brown eyes, we can infer that 18% of women also have brown eyes.
Therefore, D) 28% is the right response.
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Find each value or measure.
x = _____
mJK=_____ degrees
mMJ=_____ degrees
mLMK=______ degrees
(30 points) will give brainiest for effort
The value or measure of following are :-
x = 17.18°
∠JK = 143.78°
∠MJ = 116.48°
∠LMK = 47.17°
What is an arc?A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.
Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:
∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°
∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°
We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:
∠MNJ = ∠LNK
The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:
½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK
2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ
11x - 9° = 2∠MNJ
∠MNL = ∠JNK
The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:
½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK
2.75x + 1.5° = 2∠JNK
1.375x + 0.75° = ∠JNK
Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:
2∠MNJ + 2∠JNK = 360°
Substituting the expressions we found for ∠MNJ and ∠JNK, we get:
22x - 18° = 360°
22x = 378°
x = 17.18° (rounded to two decimal places)
Now that we know x, we can find the values of the other angles of arc-
∠JNK = 1.375x + 0.75° = 24.43°
∠KNL = 8.5x - 20.5° = 119.35°
∠MNJ = (11x - 9°)/2 = 92.05°
∠LNK = ∠MNJ = 92.05°
∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°
∠JK = ∠JNK + ∠KNL = 143.78°
∠MJ = ∠MNJ + ∠JNK = 116.48°
∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°
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Please help me. Giving brainliest to whoever gets it right!!
The equation of the line is: y = 0.5x + 4 and the inequality is H > 74.25
The equation of the graphTo find the equation of a line that passes through two points, we need to use the slope-intercept form of a linear equation:
y = mx + b
The slope is calculated as
m = (y2 - y1) / (x2 - x1)
m = (11 - 4) / (14 - 0)
m = 7/14
m = 1/2
m = 0.5
Next, we have
y = mx + b
4 = 0.5(0) + b
b = 4
So the equation of the line is: y = 0.5x + 4
Jacy's music downloadPart A: The equation that could be used to find the value of s is:
12s + 5.04 = 15.48
To find the value of s, we need to isolate the variable on one side of the equation.
We can do this by subtracting 5.04 from both sides and then dividing both sides by 12:
12s + 5.04 - 5.04 = 15.48 - 5.04
12s = 10.44
s = 10.44/12
s = 0.87
Therefore, Jacy paid $0.87 to download each song.
Tara's inequalityTo represent the number of hours, h, that Tara plans to work this month as an inequality, we can use the fact that she plans to work more hours than last month.
Let H be the total number of hours that Tara works this month.
Then we can write:
H > 16.5 + 19 + 23 + 15.75
Simplifying the right-hand side, we get:
H > 74.25
Therefore, the inequality that represents the number of hours, h, Tara plans to work this month is: H > 74.25
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Solve: 24b=6
A b=1/6
B b=1/2
C b=1/3
D b=1/4
Answer:
D. b=1/4
Step-by-step explanation:
Use square roots to solve the equation x^2=-64
Answer:
x equals 8 due to 8^2 being 8x8=64
Step-by-step explanation:
Help fast please, it should be asap please
The function has a vertical asymptote at x = 1, x-intercepts are x = 1 and x = 5, hole at x = 5 and horizontal asymptote is y = 0.
Define rational functionA rational function is a function that can be expressed as the ratio of two polynomial functions. In other words, it is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to zero for any value of x.
To plot the rational function f(x) = (x² - 6x + 5)/(-x + 1)
Vertical asymptote: The denominator of the function (-x + 1) is equal to zero when x = 1.
Therefore, there is a vertical asymptote at x = 1.
x-intercept: To find the x-intercept, we set the numerator equal to zero and solve for x:
x² - 6x + 5 = 0
This quadratic equation can be factored as:
(x - 5)(x - 1) = 0
Therefore, the x-intercepts are x = 1 and x = 5.
y-intercept: To find the y-intercept, we set x equal to zero:
f(0) = (0² - 6(0) + 5)/(-0 + 1) = 5
Therefore, the y-intercept is (0, 5).
Hole: The function has a hole at x = 5 because both the numerator and the denominator become zero at x = 5.
Horizontal asymptote: To find the horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of the numerator is 2 and the degree of the denominator is 1, so the horizontal asymptote is y = 0.
Now, we can plot the function by choosing some values of x and calculating the corresponding values of y:
x y = f(x)
-1 4
0 5
0.5 3.25
1 undefined
2 -1
Image is attached below.
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1,5/2,25/4 6th term.
Answer:
3125
32
Step-by-step explanation:
[tex]formula = a {r}^{n - 1?} [/tex]
r=5
2
a=1
n=6
1×5 (6-1)
2
5 (5)
2
=3125
32
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Answer: 0.6954
Step-by-step explanation:
To find the area between two z scores, in this case P(-0.82<z<1.29), we can either use a z score calculator or a standard normal distribution table, which I will use for this.
The probability of P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82).
To find P(z<2.01), we use a positive z score standard normal distribution table and find that P(z<1.29)=0.9015
Using a negative z score standard normal distribution table, we can find that (z<-0.82)=0.2061.
So, P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82)=0.6954.
In a certain trail mix, 65% of the total weight is made up of nuts. Of that 65%, 3/5 of the nuts are cashews. If the total weight of the trail mix is 200 grams, how many grams are cashews?
There are 78 grams of cashews in the trail mix.
What is weight?
Weight is the measure of the gravitational force exerted on an object due to its mass. It is commonly measured in units of mass, such as kilograms or pounds. Weight can vary depending on the gravitational pull of the planet or other celestial body on which the object is located. For example, an object that weighs 100 kilograms on Earth would weigh less on the Moon due to the Moon's lower gravitational force. It is important to distinguish between weight and mass, as they are not the same thing. Mass is a measure of the amount of matter in an object, whereas weight is a measure of the force exerted on an object by gravity.
If 65% of the total weight is made up of nuts, then the weight of nuts in the trail mix is 0.65 × 200g = 130g
Out of the 130g of nuts, 3/5 are cashews. So the weight of cashews in the trail mix is (3/5) × 130g = 78g
Therefore, there are 78 grams of cashews in the trail mix.
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5. Apply Math Models A science teacher uses a fair spinner
simulate choosing 1 of 5 different field trips for her classes.
spinner has 5 equal sections, each representing a different
trip. The teacher spins the spinner 50 times and records the
results in the table below.
Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.
What is frequency?
Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).
The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.
The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.
The experimental and theoretical probabilities do not match exactly. For example, the experimental of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.
The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.
Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).
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Commplete Question:
A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:
Field Trip Number of times selected
A 8
B 16
C 9
D 12
E 5
Apply math models to analyze the data and answer the following questions:
What is the experimental probability of selecting each field trip?
What is the theoretical probability of selecting each field trip?
Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?
What is the relative frequency of selecting each field trip?
Based on the data, which field trip appears to be the most popular?
Express answers in terms of pi.
1. The radius of a cylinder is 10; the height is 2. Find:
a. circumference of the base
b. area of the base
c. L.A.
d. T.A,
e. V
2. Repeat Excercise 1, using a cylinder in which r = 2 and h = 10.
a. b. c. d. e.
Answer:
1 b
2.c
ythis the best choice
The circumference and the areas and the volumes are calculated below
Calculating the circumference and the areasFor a cylinder with a radius of 10 and a height of 2:
a. The circumference of the base is 2πr = 2π(10) = 20π.b. The area of the base is πr² = π(10)² = 100π.c. The lateral area is 20π(2) = 40π.d. The total surface area is the sum of the lateral area and the areas of the two bases. 2πr² + 2πrh = 2π(10)² + 2π(10)(2) = 400π + 40π = 440π.The volume of the cylinder is given by the formula V = πr²h = π(10)²(2) = 200π.For a cylinder with a radius of 2 and a height of 10:
a. The circumference of the base is 2πr = 2π(2) = 4π.b. The area of the base is πr² = π(2)² = 4π.c. The lateral area is 4π(10) = 40π.d. The total surface area is 2πr² + 2πrh = 2π(2)² + 2π(2)(10) = 8π + 40π = 48π.e. The volume of the cylinder is given by the formula V = πr²h = π(2)²(10) = 40π.Read more about circumference at
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What is the volume of a box that is 3 feet tall, 5 feet wide, and 6 feet long
Answer:
90 cubic feet
Step-by-step explanation:
3 feet × 5 feet × 6 feet = 90 cubic feet
A right rectangular prism has a base with an area of 25 1/2 square feet and a volume of 153 cubic feet. What is the height, in feet, of the right rectangular prism? Please help!!
Answer:
[tex]25.5h = 153[/tex]
[tex]h = 6[/tex]
The height is 6 feet, so A is correct.
12x + 2y, when x = 7 and y = 8 help me please
Answer:
100
Step-by-step explanation:
12x + 2y ← substitute x = 7 and y = 8 into the expression
= 12(7) + 2(8)
= 84 + 16
= 100
what is the weight of a 38kg child
A particular sound wave can be graphed using the function y= -1sin 5x. Find the period of the function
Answer:
The period of a sine function of the form y = a sin bx is given by:
period = (2π) / |b|
In this case, the function is y = -1 sin 5x, which can be rewritten as y = -sin(5x). So, we can see that b = 5.
Substituting b = 5 into the formula, we get:
period = (2π) / |5|
period = π / 5
Therefore, the period of the function is π/5.
Find the surface Area
Math step by step Answer
(a) The total surface area of the triangular prism is 560 in².
(b) The surface area of the cuboid is 944 ft².
(c) The surface area of the cylinder is 678.58 in².
What is the surface area of the cuboid, cylinder and prism?Cuboid;
The surface area of the cuboid is calculated as;
S.A = 2(12 x 16 + 12 x 10 + 16 x 10)
S.A = 944 ft²
Cylinder:
The surface area of the cylinder is calculated as follows;
S.A = 2π x 6 (6 + 12)
S.A = 678.58 in²
The surface area of a triangular prism can be calculated by summing the areas of its individual faces.
A triangular prism has three rectangular faces and two triangular faces.
The formula for the surface area of a triangular prism is:
Surface Area = Area of triangular faces + Area of rectangular faces
To calculate the area of a triangular face, we can use the formula for the area of a triangle:
Area of a triangle = (base × height) / 2
Given that S₁ = 8 in, S₂ = 12 in, S₃ = 8 in, and the length between the two triangular faces is 18 in, we can proceed with the calculations.
The area of the triangular face with dimensions S₁ = 8 in and S₂ = 12 in is:
Area of triangular face 1 = (8 in × 12 in) / 2 = 48 in²
The area of the triangular face with dimensions S₂ = 12 in and S₃ = 8 in is:
Area of triangular face 2 = (12 in × 8 in) / 2 = 48 in²
The area of the triangular face with dimensions S₃ = 8 in and S₁ = 8 in is:
Area of triangular face 3 = (8 in × 8 in) / 2 = 32 in²
Now, let's calculate the area of the rectangular faces.
Area of rectangular face 1 = 18 in × 12 in = 216 in²
Area of rectangular face 2 = 18 in × 12 in = 216 in²
Finally, we can sum up all the areas to get the total surface area of the triangular prism:
Surface Area = Area of triangular faces + Area of rectangular faces
Surface Area = 48 in² + 48 in² + 32 in² + 216 in² + 216 in² = 560 in²
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Part 1: Hitting a golf ball into a tower? While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air. 1. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Since the maximum height h is equal to 225 ft which is close to 300 ft we can conclude that Marc hit the ball near the top of the tower.
The maximum point of the quadratic function :The concept used in this problem is the quadratic function and finding the maximum or minimum value of a quadratic function.
The x-coordinate of the vertex, which is the highest or lowest point on the graph, can be found using the formula:
=> x = -b / 2a
Here we have
The formula for the shot is h(x) = -16xsquared + 120x,
Where h is the height of the ball and x is the number of seconds the ball is in the air.
To mathematically prove that Marc hit the ball near the top of the tower, find the maximum height reached by the ball and compare it with the height of the tower.
To find the maximum height reached by the ball, find the vertex of the parabolic function h(x).
As we know
The x-coordinate of the vertex is given by:
x = -b / (2a)
Where a and b are the coefficients a and b
In this case, a = -16 and b = 120, so we have:
x = -120 / (2(-16)) = 3.75 seconds
The maximum height reached by the ball is given by:
h(3.75) = -16(3.75)² + 120(3.75) = 225 feet
To prove that Marc hit the ball near the top of the tower, we need to compare the maximum height reached by the ball (225 feet) with the height of the tower (300 feet).
Since the ball hit near the top of the tower, we can assume that it was close to the highest point of the tower when it was hit.
Therefore,
Since the maximum height h is equal to 225 ft which is close to 300 ft we can conclude that Marc hit the ball near the top of the tower.
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Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
A walk alongside a railway track is represented on a map by an 86 mm straight line.
The walk is 17.2 km.
What is the scale of the map?
First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.
Don has an album that holds 700 photos. Each page of the album holds 7 photos. If 24% of the album is empty, how many pages are filled with photos?
Answer: 76 pages
Step-by-step explanation:
700 photo spaces = 100%
-The total
168 photo spaces = 24%
-The number of empty spaces in the album.
- Find 24% of 700:
70(10%) x 2 = 140
7(1%) x 4 = 28
140 + 28 = 168
532 photo spaces = 76%
- The number of photos in the album
700 - 168 = 532
Finding the number of pages.
-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.
532 ÷ 7 = 76.
7. Fill in the bubbles to indicate whether
each expression is linear or not linear.
5x Linear or Nonlinear
6x+1 Linear or Nonlinear
10xy Linear or Nonlinear
17 Linear or Nonlinear
4x^2 Linear or Nonlinear
The type of the relation are
Linear: 5x, 6x + 1 and 16Nonlinear: 10xy and 4x^2Indicating whether each expression is linear or not linearA linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.
In the given expressions:
"5x" and "6x + 1" have only the variable "x" raised to the power of 1, making them linear."10xy" has the variables "x" and "y" both raised to the power of 1, making it nonlinear."17" is a constant term and has a degree of 0, making it linear."4x^2" has the variable "x" raised to the power of 2, making it nonlinear.Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".
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Liam is making 8 sculptures. Each
sculpture needs yard of wire for the
base and another piece of wire for the
top. He uses 10 yards of wire in all.
How much wire is needed for the top of
each sculpture?
Liam needs 0.25 yards of wire for the top of each sculpture.
How much wire is needed for the top of each sculpture?Let's assume that Liam needs x yards of wire for the top of each sculpture.
Since Liam is making 8 sculptures, he will need 8x yards of wire in total for the tops of all the sculptures.
We also know that Liam needs one yard of wire for the base of each sculpture.
So he will need 8 yards of wire in total for the bases of all the sculptures.
Therefore, the total amount of wire Liam needs is:
8x yards for the tops + 8 yards for the bases = 10 yards in total
Simplifying this equation, we get:
8x + 8 = 10
Subtracting 8 from both sides, we get:
8x = 2
Dividing both sides by 8, we get:
x = 0.25
Therefore, Liam needs 0.25 yards of wire for the top of each sculpture.
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Michelle did an anyonymous survey and collected her friends' credit scores. The scores she found are listed in the table below. What is the
mean credit score in this group? (Round to the nearest whole point, if applicable.)
a. 698
b. 695
c. 676
d. 703
to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
The probability that a person has the virus given that they have tested positive is 3.24%.
The probability that a person does not have the virus given that they test negative is 99.93%.
What is Probability?Here we have following probabilties:
P(A)=1/300, P(A')=1-(1/300)=299/300
P(B|A)=0.80, P(B|A')= 0.08
From the law of total probability is
P(B)=P(B|A)P(A)+P(B|A')P(A')
[tex]=0.80\cdot \frac{1}{300}+0.08\cdot \frac{299}{300}\\\\=0.0824[/tex]
By the Baye's theorem we have
P(A|B) = [tex]\frac{P(B|A)P(A)}{P(B)}\\\\=\frac{0.80\cdot \frac{1}{300}}{0.0824}\\\\=0.0324[/tex]
So the probability that a person has the virus given that they have tested positive is 3.24%.
(b)
From the law of total probability is
P(B')=P(B'|A)P(A)+P(B'|A')P(A')
[tex]=0.20\cdot \frac{1}{300}+0.92\cdot \frac{299}{300}\\\\=0.9176[/tex]
By the Baye's theorem we have
P(A'|B')=[tex]\frac{P(B'|A')P(A')}{P(B')}\\\\=\frac{0.92\cdot \frac{299}{300}}{0.9176}\\\\=0.9993[/tex]
So the probability that a person does not have the virus given that they test negative is 99.93%.
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Suppose you want to make your own model of the geologic time scale. You decide to make a timeline with a scale of 1 centimeter equals 1 million years. Remember that 100 cm is equal to 1 meter, which is a little longer than 3 feet.
A timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.
What is the unit conversion?
Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement that is equivalent in value. The need for unit conversion arises because different units are used to measure the same physical quantity in different countries or regions, or in different fields of study.
Making a model of the geologic time scale with a scale of 1 centimeter equals 1 million years means that each centimeter on the timeline represents 1 million years of geologic time.
To create the model, we can start by determining the total length of the timeline we want to create.
Let's say we want to include the entire Phanerozoic Eon, which spans approximately 541 million years.
To represent this on our timeline, we would need a total length of 541 centimeters.
However, we need to keep in mind that 100 cm is equal to 1 meter, which is a little longer than 3 feet.
Therefore, a timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.
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