[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]
Evan picks up a cantaloupe that weighs 3.24 pounds. Suppose Evan
could buy 100 cantaloupes that are all this weight. Without using the
multiplication algorithm, explain how Evan could figure out the total
weight of all 100 cantaloupes.
The total weight of the 100 cantaloupe is 324 pounds
How to determine the total weight?The given parameters are:
Weight of each = 3.24 poundsNumber of cantaloupe = 100Since the number of zeros in 100 is 2;
All Evans needs to do is to move the decimal point in 3.24 two places forward.
i.e. 3.24 becomes 324 when the decimal point is moved
Hence, the total weight of the 100 cantaloupe is 324 pounds
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Solve the following inequality algebraically:
-2 less-than x/3 + 1 less than 5
a.
Negative 9 greater-than x greater-than 12
b.
Negative 9 less-than x less-than 12
c.
Negative 2 less-than x less-than 5
d.
Negative 2 greater-than x greater-than 5
Answer:
d
Step-by-step explanation:
In a P.7 class, 20% of the boys were absent for the Mock Examinations, of the remainder of the boys were present Find the fraction of the girls in the class.
One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know that the perimeter of the rectangle is 58 meters
Answer:
22 meters
Step-by-step explanation:
Let x = width of the rectangle
Let y = length of the rectangle
Equation 1
If the length of the rectangle is 6 meters shorter than four times the width then:
⇒ y = 4x - 6
Equation 2
Perimeter of a rectangle = 2(width + length)
If the perimeter is 58 inches, then:
⇒ 58 = 2(x + y)
Solve by substitution
Substitute Equation 1 into Equation 2 and solve for x:
⇒ 58 = 2(x + 4x - 6)
⇒ 58 = 2(5x - 6)
⇒ 58 = 2 · 5x - 2 · 6
⇒ 58 = 10x - 12
⇒ 58 + 12 = 10x -12 + 12
⇒ 10x = 70
⇒ 10x ÷ 10 = 70 ÷ 10
⇒ x = 7
Substitute found value of x into Equation 1 and solve for y:
⇒ y = 4(7) - 6
⇒ y = 28 - 6
⇒ y = 22
Conclusion
The dimensions of the rectangle are:
width = 7 meterslength = 22 metersTherefore, the length of the longer side is 22 meters
The length of the longer side is 22 meters.
Let, one side of the rectangle is x meters.
According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is 58 meters:
58 = 2 * (x + 4x - 6)
Now, let's solve for x:
58 = 2 * (5x - 6)
58 = 10x - 12
Add 12 to both sides:
58 + 12 = 10x
70 = 10x
Now, divide both sides by 10 to isolate x:
x = 70 / 10
x = 7
So, one side of the rectangle is 7 meters.
Now, we can find the length of the longer side:
Length of the longer side = 4x - 6
Length of the longer side = 4 * 7 - 6
Length of the longer side = 28 - 6
Length of the longer side = 22 meters
Therefore, the length of the longer side is 22 meters.
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What is the volume, in cubic meters of the prism below?
Answer:
1848 Cubic Meters
Step-by-step explanation:
The volume should be (7*24*22)/2
This is because this object is bascally half of a rectangular prism, so we need to divide the whole product by 2 at the end.
7*24*22 = 3696
3696/2 = 1848
Please pick one of the options.
9880 different possibilities are there in Sally's new combination option second 9880 is correct.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Total unique numbers consists in a Sally locker = 3
From the digits 0 to 39
Total numbers = 40
Apply combination formula:
= C(40, 3)
= 40!/(3!37!)
= 9880
Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.
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the diagram shows a right angled triangle. 9cm 15cm x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
Answer:
31°
Step-by-step explanation:
As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.
=============================================================
Solving :
⇒ tan x° = 9/15
⇒ tan x° = 3/5
⇒ x = tan⁻¹ (0.6)
⇒ x = 31°
The size of the unknown angle "x"
Solution:We'll have to check which is the appropriate one from SOHCAHTOA.
In this question we'll have to use tan because opposite and adjacent is given.
[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]
Substitute according to the formula.
[tex]tan \: x= \frac{9}{15}[/tex]
We'll have to use tan inverse.
[tex]x={tan}^{-1}(\frac{9}{15})[/tex]
[tex]x=30.96375653[/tex]
[tex]\large\boxed{x=31° }[/tex]
Hence, the size of the unknown angle "x" is 31°
Write the standard number.
3.6 * 10^-6
Answer:
The answer is 0.0000036.
Step-by-step explanation:
Move the decimal place 6 spaces to the left. I hope this helps! :)
This is super easy. Explanation, please!
The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).
How to analyse a operation between two functions by propositional approach
In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).
We must check if the proposition is true for every ordered pair. Let analyze each case:
Case I
[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]
Case II
[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]
Thus, the proposition is false.
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Which sentence correctly compares the two numbers 5.395 and 5385 ?
5.395= 5385
5.385 > 5.395
5395< 5.385
5385 < 5.395
The sentence that correctly compares the two numbers is 5385 > 5.395
What is the correct sentence?Here are inequality signs and what they mean:
Note that
5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.
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27
C
A
54
B
Based on the diagram, which expresses all possible
lengths of segment AB?
O AB = 25
O 27
OAB = 85
O AB< 27 or AB > 81
Answer:
B. 27 < AB < 81
Step-by-step explanation:
The triangle inequality requires that the length of any given side of a triangle be greater than the difference and less than the sum of the other two sides.
__
application54 -27 < AB < 54 +27
27 < AB < 81
_____
Additional comment
Some versions of the triangle inequality allow the "or equal to" case.
27 ≤ AB ≤ 81
Apparently, the one used here does not.
If the sum of the two short sides is equal to the long side, the "triangle" looks like a line segment. Its altitude and area are zero.
You roll a number cube. What is the probability it will land on a number greater than 5?
Which of the following points is not coplanar with points C, D and E?
The point R is the point which is not coplanar with points C, D and E.
We need to find the point which is not coplanar with points C, D and E.
What are coplanar points?The points that lie on the same plane are called coplanar points.
In the given figure there are five planes which are as follows:
BCUD, BRAE, BRAC, BTDE, ACUDE
Now, points C,D and E lie in plane ACUDE.
In the plane ACUDE points A, C, U, D, E and S lies.
From the options point, R is not lining in the same plane as C, D and E lies.
Therefore, the point R is the point which is not coplanar with points C, D and E.
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A rectangular swimming pool is 15 meters long, 14 1/2 meters wide, and 3 1/2 meters deep. What is its volume? in cubic meters
Answer:
761.25 m³
Step-by-step explanation:
l = 15 , w = 14.5 , h = 3.5
Volume of a rectangular prism is given by the formula :
V = lwh
V = 15 × 14.5 × 3.5
V = 761.25
Units will be m³
I am attaching an image for visual understanding
Hope this helped and brainliest please.
What is (f−g)(x) ?
f(x)=x3−3x2+2x−3
g(x)=4x2−5x+7
Enter your answer in the box.
(f−g)(x)=
Answer:
Step-by-step explanation:
(F-G)(X)=x^4-x^3+2x-6
The ________________ measures the spread of the middle 50% of the data set.
A. median
B. range
C. interquartile range
D. mode
Answer:
C. interquartile range
Step-by-step explanation:
using this to show im right
"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."
Hope This Helped
Which property justifies the following if angle A is congruent to angle B and angle b is congruent to angle C then angle a is congruent to angle c
Answer: Transitive property of congruence
6. Janet spent $25, $30, $10, and $8 for
recreation in the last four weeks. What
was her average weekly expense for
recreation?
A. $12.50
B. $18.25
C. $25.25
D. $36.50
Answer:
B
Step-by-step explanation:
Total money spent = 25 + 30 + 10 + 8 = 73
Per week = 73 / 4 = 18.25
HELP ASAP!!!!! The graph compares temperatures and numbers of cyclists. The equation of the trend line for the scatterplot is y = 4x + 10. Predict the number of cyclists when the temperature is 12°C.
So
Put x ax 12°CHence
y=4(12)+10y=48+10y=58Option A
Answer:
Option A
Step-by-step explanation:
y=4x+10
So
Put x ax 12°C
Hence
y=4(12)+10
y=48+10
y=58
15 ( y - 4 ) - 2 (y - 9 ) + 5 (y + 6) = 0
Answer:
y = 2/3
Step-by-step explanation:
Assuming you are looking for "y":
15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0
15y - 60 - 2y + 18 + 5y + 30 = 0
15y - 2y + 5y -60 + 18 + 30 = 0
18y = 60 - 18 - 30
18y = 12
y = 12/18
y = 2/3
Follow the steps below for the following set of data. In your final answer include all of your calculations and all work in steps 1, 2, and 3.
8, 3, 5, 5, 4, 7
Find the median, lower quartile, and upper quartile of the set of data.
Use the median, lower quartile, upper quartile, lowest value, and highest value of the set to construct a box-and-whisker plot on your own sheet of paper.
Use the box-and-whisker plot to find the range and the interquartile range of the set of data.
The answers to the question are
Median = 5Lower quartile = 4Upper quartile = 7What is the median?The median of the data set is gotten by arranging the values in order
3, 4, 5, 5, 7, 8
The median can be gotten by
5 + 5 / 2
= 10/2
Median = 5
What is the lower quartile?This is the value under which 25 percent of the data are found in the group of data. The lower quartile is 4.
What is the upper quartile?This is the point from which 75 percent of the data is found when it is in ascending order. The upper quartile is 7.
What is the lowest valueThe lowest value in the data set is 3
What is the highest valueThe highest value in the data set is 8
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At her sisters birthday party Cheyenne thought it would be funny to drink lemonade from a party hat if the radius is 4.8 cm and the height of a hat is 12 cm how many cubic centimeters of lemonade can Cheyenne pour into the hat
92.16 pi cm^3.
Step-by-step explanation:
Shape of a party hat : conical
Volume of a cone = (1/3)(pi)(r^2)(h)
(pi(1/3)(23.04)(12))cm^3
Therefore, approximately
92.16 pi cm^3.
If f(x) = 3x +3, which of the following is the inverse of f(x)?
O
A. f-1(x) = 3(x-3)
5
OB. f-1(x) = 3(x+3)
5
O C. f-1(x) = 5(x+3)
3
O D. f-1(x) = 5(x-3)
3
The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
How to determine the inverse?The equation is given as:
f(x) = 3x + 3
Express f(x) as y
y = 3x + 3
Swap the positions of y and x
x = 3y + 3
Make y the subject
3y = x - 3
Divide by 3
y = 1/3x - 1
Replace y with the inverse function
f-1(x) = 1/3x - 1
Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
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What is 5 over 8 expressed as a percent?
Answer: 62.5%
Step-by-step explanation:
5/8 = 0.625
0.625 x 100 = 62.5
tn=2(n-1)
Given the formula for the nth term, state the first 5 terms of each sequence.
Answer:
0, 2, 4, 6, 8
Step-by-step explanation:
substitute 1 for n in first term, 2 for n in second term, 3 for n in third term, 4 for n in fourth term, 5 for n in fifth term
2 (1) -2 = 0 first term
2 (2)-2 = 2 second
2 (3)-2 = 4 third
2 (4)-2 =6 fourth
2 (5)-2 =8 fifth
Solve for x: -24 = 6x
1/4
-4
4
- 1/4
Answer:
-4
Step-by-step explanation:
[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]
Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.
Answer: AAS
Step-by-step explanation:
We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.
Find the circumference of a circle that has a diameter of 2 ft. Use 3.14 for pi.
5.14 ft
6.28 ft
12.56 ft
7.14 ft
Answer:
6.28 ft
Step-by-step explanation:
using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer
If one student is chosen at random, Find the probability that the student was NOT a female that got a "C"
--------- A // B // C // Total
Male: 10 // 8 // 15 // 33
Female: 7 // 9 // 17 // 33
Total: 17 // 17 // 32 //66
The probability that the student was NOT a female that got a "C" is 15 / 32.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C = 15 / 32.
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a. The velocity, v, of an object is moving in a medium at time t is given by
t = √ 30² +50+2 du. Evaluate t.
+
The value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
Velocity of the object moving in the medium
The velocity of the object moving in the medium is given as;
t = ∫(3u² + 5u + 2)du
the value of t is obtained by integrating the function as follows;
t = (3u³)/3 + (5u²)/2 + 2u
t = u³ + 2.5u² + 2u
Thus, the value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
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