Answer:
There are 78 plums and 42 peaches.
Step-by-step explanation:
Let p = number of plums.
Let e = number of peaches.
The value of the plums is 2p.
The value of the peaches is 3e.
"total cost of plims was 30$ more than the cost of peaches"
2p = 3e + 30
"there are 120 fruits some are plums [...] others are peaches"
p + e = 120
We have a system of simultaneous equations.
2p = 3e + 30
p + e = 120
2p = 3e + 30
p = -e + 120
2p = 3e + 30
+ 3p = -3e + 360
------------------------------
5p = 390
p = 78
p + e = 120
78 + e = 120
e = 42
Answer: There are 78 plums and 42 peaches.
Check:
78 plums cost 78 × $2 = $156
42 peaches cost 42 × $3 = 126
$156 - $126 = $30
The plums do cost $30 more than the peaches.
78 + 42 = 120
The total is indeed 120.
The answer above is correct.
which sample will have a larger chi-square test statistic? (see if you can tell without doing any calculations.)
The sample with more observations and/or more variability in the data will generally have a larger chi-square test statistic.
Chi-square test statistic is a measure of how well a set of observed data fits a theoretical model. The larger the sample size and the more variability in the data, the more likely it is that the theoretical model won't fit the data perfectly. Therefore, the larger sample size and variability in the data will lead to a larger chi-square test statistic.
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Write the log equation as an exponential equation. You do not need to solve for x.
log_5x(2x-4)=3x+2
If the value of the base is y, then y^(3x+2) = 5x(2x-4)
What is logarithm?logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x= n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log8 base 2.
Also if 10² = 100 , then 2 = log100 base 10.
representing the unknown base to be y
then, log 5x(2x-4) base y = 3x+2
from the law of logarithm
log a base b = x, then b = a^x
Similarly log 5x(2x-4) base y = 3x+2
then 5x(2x-4) = y^(3x+2)
Therefore the exponential equation of the logarithm is 5x(2x-4) = y^(3x+2)
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the angle of elevation of the sun is decreasing at a rate of 0.25 radyh. how fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the sun is ?y6?
The shadow of a 400ft tall building is increasing at a rate of 100ft /hr
The angle of elevation of the sun is decreasing at a rate of 0.25 rad/hr
The height of the building is 400 ft tall
We need to find the rate at which the shadow is increasing
d/dθ = 1/4 rad/hr at θ = π/4
400/x = tan θ
x = 400/ tan θ
Upon derivation with t
dx/dt = 400 sec²θ/tan ²θ dθ/dt
at θ = π/4 and dθ/dt = 0.25 rad/hr
dx/dt = 400 (2x3)x0.25
dx/dt = 100ft/hr
Therefore, the shadow is increasing at the rate of 100ft/hr
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What is the third quartile of the given data set?
(2,5,6,7,15, 16, 17)
Answer:
16 is the third quartile
please help me with question no. 5
If possible then answer with an explanation would be appreciated.
Answer:
a)
Step-by-step explanation:
additions do not work in general that way when we consider a mixture of positive and negative numbers.
e.g.
x = 3, y = -5
|3 + -5| >= |3| + |-5|
|-2| >= 3 + 5
2 >= 8
is definitely not true.
so, for positive/negative number mixtures a) is wrong.
b) works because
if x >= y, then |x - y| >= |x| - |y|. equal when x and y > 0. larger when x and/or y < 0. correct
if x < y, then |x - y| >= |x| - |y|. larger when x and y > 0.
equal when x and/or y < 0.
c) and d) work because the signs don't change anything. either the result is positive anyway, or if negative just gets converted to the positive result.
Find the value of the variable
A. 74 degree
B. 64 degree
C. 32 degree
D. 180 degree
Please help!!!
Answer:
A, 74°
Step-by-step explanation:
Both of the angles are named y, so this means they are the same/have the same value!
Remember, all triangles equal 180°
To find y...
First, we subtract 32° from 180° to see what the Y angles total up to!
180° - 32° = 148°
the two y angles on the left side of the triangle equal 148°, but what does just one of them equal?
Divide by 2 to find out!
148° ÷ 2 = 74°
one y angle = 74°
y = 74°
(q014) how many of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise?
five out of of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise
If you were to attribute this film, that means you'd say that (something) caused the success of the movie Rocky. This question is basically asking what do you think made this movie a big hit? Personally, I'd say it's because of how the storyline and plot turned out. It's very intriguing and it doesn't just make the movie about boxing. The film adds some love between the protagonist and some other character, and not only that, but the movie teaches you something. Because Rocky lost to Apollo, Rocky didn't care. At least he still had Adrian. So, the movie teaches you that, even if you do lose, at least you still have something and/or someone with you.
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Which graph represents the inequality y > 3-x?
A ship sails 40 nautical miles (nm) due west from point A and then changes course and sails 20 nautical miles in a direction that is 54° west of due north. A diagram of the ship’s trip is shown
A. Find m
B. Find the length of b to the nearest hundredth
.
C. the length of d to the nearest hundredth.
D.the distance from point A to point C.
E. Find m
F. the length of c to the nearest nautical mile (nm).
Answer:
Look at pic 2 for the measurements. I rounded to the thousandth, because some required rounding to the hunderedth and others required to the nearest mile and others were unspecified.
Step-by-step explanation:
We should first draw a diagram. Since you said a diagram is shown, I will assume that the diagram looks something like pic 1. I do not know which variables correspond to which lengths, so I used random variables, but the diagram I drew should help you figure out which variables I used correspond to your actual problem.
If so, we can use our trigonometric functions and Pythagorean theorem to solve for all the lengths
We must solve for x and y in the diagram, and we can do so by using sine and cosine. We know the orange angle of the triangle whose legs are x and y is 36 degrees. We also know the hypotenuse of that triangle is of length 20 nm. Thus, [tex]sin(36) = \frac{x}{20}[/tex] and [tex]cos(36) = \frac{y}{20}[/tex].
We can multiply both sides of both of these functions by 20 to get: [tex]x = sin(36) * 20[/tex] and [tex]y = cos(36) * 20[/tex]. These are approximately x = 11.756 nautical miles and y = 16.180 nautical miles
We can solve for the length of a by adding 40 to y and getting a = 16.180 + 40 = 56.180 nautical miles
We can solve for the length of z by using the Pythagorean theorem and the leg lengths of a and x. We can do [tex]\sqrt{(40 + 20cos(36))^2 + (20sin(36))^2}[/tex] and get z = [tex]\sqrt{3294.427191}[/tex] = 57.397 nautical miles
Thus, we get the measurements in pic 2 as the distances you are asked to solve for.
The lengths are 56.180 nautical miles and 57.397 nautical miles
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse.
Given that, A ship sails 40 nautical miles (nm) due west from point A and then changes course and sails 20 nautical miles in a direction that is 54° west of due north.
We can use our trigonometric functions and Pythagorean theorem to solve for all the lengths
We must solve for x and y in the diagram, and we can do so by using sine and cosine. Furthermore, we also know the hypotenuse of that triangle is of length 20 nm. Thus, and.
We can multiply both sides of both of these functions by 20 to get: and. These are approximately x = 11.756 nautical miles and y = 16.180 nautical miles.
We can solve for the length of a by adding 40 to y and getting a = 16.180 + 40 = 56.180 nautical miles
We can solve for the length of z by using the Pythagorean theorem and the leg lengths of a and x. Likewise, we can do √40+(20cos(36°)²)+(20sin36°)²) and get z = 57.397 nautical miles.
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f ''(x) = x−2, x > 0, f(1) = 0, f(8) = 0
The required function f when f"(x) = x^-2, x > 0, f(1) = 0, f(2) = 0 is f(x) = - ln x + (ln 8) x/7 + (ln 8)/7
In tthis question we have been given the second derivative of function
f"(x) = x^-2, x > 0, f(1) = 0, f(2) = 0
We need to find a function f(x).
Consider f"(x) = x^-2
Integrating above expression with respect to x we get,
f'(x) = -1/x + C
againg integrating above expression with respect to x we get,
f(x) = - ln x + Cx + D
Now we need to find C and D.
Given that f(1) = 0
- ln (1) + C + D = 0
C + D = 0 ........... (1)
And f(8) = 0
- ln 8 + 8C + D = 0
8C + D = ln 8 ..............(2)
subtracting equation (1) from equation (2),
C = (ln 8)/7
Subtituting above value of C in equation (1) we get,
D = -(ln 8)/7
So, f(x) = - ln x + (ln 8) x/7 + (ln 8)/7
Therefore, the required function : f(x) = - ln x + (ln 8) x/7 + (ln 8)/7
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5. Find the range of values of x for which (3x-7)(x-5) ≥x+5.
Answer: Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).
Step-by-step explanation: To find the range of values of x for which (3x-7)(x-5) ≥x+5, we first need to find the values of x for which the inequality is satisfied. We can do this by setting each factor equal to 0 and solving for x.
Setting (3x-7) equal to 0 gives us x=7/3. Setting (x-5) equal to 0 gives us x=5.
Next, we need to consider the signs of the factors. If both factors are positive or both are negative, the inequality will be satisfied. If one factor is positive and the other is negative, the inequality will not be satisfied.
For x<5, both factors are negative, so the inequality is satisfied. For x>5, both factors are positive, so the inequality is satisfied.
Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).
Anjum and Betty spent a total of 9 hours completing the puzzle.
The ratio Anjum’s time : Betty’s time = 7 : 5.
Work out how much time Anjum spent on the puzzle.
look at the pic and answer
Triangle KLM repreent a ection of a park et aide for picnic table. The picnic area will take up approximately 400 quare yard in the park. Triangle K L M i hown. The length of K M i 45 yard and the length of L M i 20 yard. Angle L K M i 25 degree. Trigonometric area formula: Area = One-half a b ine (C)
To the nearet yard, what amount of fencing i needed to urround the perimeter of the picnic area?
95 yard
107 yard
160 yard
190 yard
The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.
We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.
We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.
Using this in the given triangle KLM, we get:
Area = (1/2)(KL)(KM)(sin K),
or, 400 = (1/2)(KL)(45)(sin 25°),
or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.
Thus, we get KL = 42 yards.
Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.
Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
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Answer: b
Step-by-step explanation:
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which value does 50% of the data lie above, and what is it called?
48, the lower quartile
50.5, the median
56, the median
53, the upper quartile
The value that 50% of the data, as shown in the box plot, lie above and what it is called is: B. 50.5, the median
What is the Median of a Box Plot?A box plot that displays the data set has the value of the median indicated at the point where a vertical line divides the rectangular box.
The median can be referred to as the second quartile (Q2) or 50th percentile of the data set.
The median value shows that 50% of the data set is above it while 50% is below it also.
The box plot in the given image shows that the vertical line crosses the rectangular box at 50.5.
50.5 is therefore the median, and this means that 50% of the data lie above 50.5.
Therefore, the answer is:
B. 50.5, the median
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[tex]y = 2x + 7[/tex]
[tex]y = 3 - \frac{1}{2} x[/tex]
Is this parallel, perpendicular, or neither?
The rectangular floor of a classroom is 28 feet in length and 38 feet in width. A scale drawing of the floor has a length of 14 inches. What is the area, in square inches, of the floor in the scale drawing?
The area of the floor of the scale drawing and the scale factor are 72 in² and 1/2 respectively.
Actual Length = 28 feets
Actual width = 38 feets
Model width = 14 inches
The scale factor = 14/28 =1/2
The length of the model can be calculated thus :
Actual Length × scale factor
Model width = 38 × 1/2= 19 inches
The Area of a rectangle can be calculated using the relation :
Area = Length × width
Area of floor = 19 inches × 14 inches = 266 inch²
Therefore, the area of the floor of the scale drawing is 266 in²
What is area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.To learn more about area refer to:
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Write 6 1/5 as an improper fraction in its simplest
form
The mixed fraction in simplest improper fraction is 31/5.
Define the term improper fraction?A fraction that has the numerator higher than or equal to a denominator is said to be inappropriate.Proper fractions are those that are higher than 0 but a little less than 1. The numerator is lower than the denominator in appropriate fractions. An improper fraction is one that has a numerator that is greater or equal to the denominator.A wrong fraction is always bigger than or equal to one.For the stated mixed fraction;
6 1/5
To convert this in improper fraction;
= (6x5 + 1)/5
= (30 + 1)/5
= 31/5
This, the mixed fraction in simplest improper fraction is 31/5.
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Help me with this question please
Todd caught at least three times as many fish this year as he did last year. He caught 63 fish this year. Write an inequality that represents how many fish he caught last year
The requirement is represented by the inequality y≥3x, and he caught at least 21 fish last year.
What is inequality?In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.
Here,
Let y is fishes caught in this year and x be the fishes caught in last year.
y≥3x
63≥3x
x≥21
The inequality that represent the condition is y≥3x and he caught at least 21 fishes last year.
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given regular pentagon $abcde,$ a circle can be drawn that is tangent to $\overline{dc}$ at $d$ and to $\overline{ab}$ at $a.$ in degrees, what is the measure of minor arc $ad$?
The measure of minor arc is 108°
Pentagon:
A pentagon is a geometrical shape, which has five sides and five angles. Here, “Penta” denotes five and “gon” denotes angle.
If a pentagon is regular, then all the sides are equal in length, and five angles are of equal measures. If the pentagon does not have equal side length and angle measure, then it is known as an irregular pentagon.
The sum of all the interior angles for a regular pentagon is 540°.
hence,
Value of each interior angle = 540°/5
= 108°
From figure,
we have to find ∠AED
we can see ∠AED is one of the internal angle of pentagon.
so,
∠AED = 108°
The measure of minor arc is 108°
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For each relation, decide whether or not it is a function.
Domain
sky
tree
leaf
cloud
Function
Not a function
Relation 1.
Function
Not a function
Range
7
Relation 3
{(m, m),(m, d),(v, v), (v, r)}
Domain
-2
Function
Not a function
Relation 2
Function
Not a function
Range
Relation 4
{(4, z),(4, e), (3, f), (9, z)}
Answer:
Relation 1 & 2 are functions
Relation 3 & 4 are not functions
Step-by-step explanation:
For a relation to be a function every x must have one and only one y
This is not true for relation 3 which has 2 y's at x = m and 2 y's at x = v
This is also not true for relation 4 which has 2 y's at x = 4
anyone know how to do this
From the triangle, the values of a and b are 5.1 units and 4.4 units respectively
How to find the lengths of a triangle?You should know that a triangle is a polygon with three sides, three vertices, three angles whose sum of angles is 180⁰
Using the trig ratio of Cosine
CosY=Adjacent/Hypothenuse
cos31=w/6
Cross multiplying we have
6*cos31=w
w=5.1 units
Then to find b, note that /VW/=/VY/=5.1
<VYX=<VWX............... base angles of isosceles triangle WVY
Using cosine again from trig.
Cos31=b/5.1
5.1*cos31=b
simplify to get b=4.4 units
Therefore b= 4.4 units
a=90-31 (remaining 2 angles of a right angled triangle)
a=59⁰
In conclusion, the value of a=59⁰ and the value of b=4.4 units
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I need help with my math please
Answer:
B) y = 3x + 2-----------------------------------
Perpendicular lines have opposite-reciprocal slopes.
Given line has a slope of - 1/3, so the perpendicular slope is 3.
The matching choice is B.
Answer:
[tex]\textsf{B.} \quad y=3x+2[/tex]
Step-by-step explanation:
If two lines are perpendicular to each other, their slopes are negative reciprocals.
The negative reciprocal of a number is -1 divided by the number.
Given equation:
[tex]y=-\dfrac{1}{3}x+4[/tex]
The slope of the given equation is -¹/₃
Therefore, the slope of the perpendicular line is:
[tex]\implies -1 \div -\dfrac{1}{3}=-1 \times -3=3[/tex]
Therefore, the equation of the line that is perpendicular to the given equation is:
[tex]\textsf{B.} \quad y=3x+2[/tex]2/3 + 1/5
4/5 + 1/2
5/7 + 1/3
1/4 -2/5
Answer:
A. 13/15
B. 13/10
C. 22/21
D. −3/20
Step-by-step explanation:
Just make the denominators equal to each other and solve. Ask your teacher for extra help
Find the coordinates of h if x(11, -6) is the midpoint of gh and g(15, 4).
Answer:
h (7, - 16 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is
M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula
let the coordinates of h be (x, y )
here (x₁, y₁ ) = g (15, 4 ) and (x₂, y₂ ) = h (x, y )
use the midpoint formula on g, h and equate to the coordinates x (11, - 6 )
[tex]\frac{15+x}{2}[/tex] = 11 ( multiply both sides by 2 )
15 + x = 22 ( subtract 15 from both sides )
x = 7
and
[tex]\frac{4+y}{2}[/tex] = - 6 ( multiply both sides by 2 )
4 + y = - 12 ( subtract 4 from both sides )
y = - 16
then
coordinates of h = (7, - 16 )
Abdullah and Amna bought a car for $9000, Abdullah paid 45% of the $9000 and Amna paid
the rest.
b) Write down the ratio of the payments Abdullah: Amna in its simplest form.
Answer:
9 : 11
is your a nswer in it's simplest form
Step-by-step explanation:
Abdullah and Amna bought a car for $9000, Abdullah paid 45% of the $9000 and Amna paid
the rest.
b) Write down the ratio of the payments Abdullah: Amna in it's simplest form.
Abdullah paid 45% means Amna paid 55% (100% - 45% = 55%), so the Abdullah : Amna ratio is 45 : 55, let's simplify by dividing the two parts by 5 and we will have the ratio in its simplest form.
45 : 55
let's simplify
9 : 11 is your answer
You notice that the row labels in your spreadsheet are 1, 2, 3, 8, 9. Row labels 4 through 7 are missing. What could cause this?.
The various reasons why rows 4 to 7 could be missing are mentioned.
Explain the term spreadsheet?A spreadsheet is a piece of software that can store, display, and edit data that has been organized into rows and columns. One of the most used tools for personal computers is the spreadsheet. In general, a spreadsheet is made to store numerical data plus short text strings.Rows 4 to 7 may be missed for the following reasons:
Rows 4 through 7 have a chance of having incorrect or improperly structured data.Probability that rows 4 through 7 are concealed.There is a chance that the users shown in rows 4 through 7 are different from the users you are currently logged in as.Rows 4 through 7 had a chance of being erased from the sheet.Thus, these are various reasons why rows 4 to 7 could be missing.
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use this model to determine the answer what is 6÷1/5
Answer: 30
Step-by-step explanation:
6 divided by 1/5 is the same as 6/1 * 5/1
6/1 * 5/1 = 30/1
=30
30/5 = 6
Answer:
30
Step-by-step explanation:
There are a couple of ways to do this. One way is the traditional way.
[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex] Then multiply by the reciprocal
[tex]\frac{6}{1}[/tex] x [tex]\frac{5}{1}[/tex] = [tex]\frac{30}{1}[/tex] = 30
Another way that is more intuitive:
[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex] Get a common denominator of 15
[tex]\frac{90}{15}[/tex]÷[tex]\frac{3}{15}[/tex] = [tex]\frac{\frac{90}{3} }{\frac{15}{15} }[/tex]= [tex]\frac{30}{1}[/tex] = 30
Solve each problem. Explain or show your reasoning.
a. What is 25% of 160?
b. What is 39% of 200?
c. What is 150% of 32?
d. 13 is 50% of what number?
e. 18 is 120% of what number?
f. 21 is what percentage of 30?
Answer:
Step-by-step explanation:
a. 40 because 25 percent is 1/4th and 160 times 1/4=40
b. 78 because 200 times 39/100 is 78
c. 48 because 32 times 150/100=48
d. 26 because if it is 50 percent it is 1/2 of a number so just multiply
e. 15
f. 70 percent, simplify both numbers to the lowest number possible equal to 21/30 so 7/10 and that is 70 percent