Answer:
0.34
Step-by-step explanation:
4 or below go down low
5 or above fly like a dove
so the 33 part is lower than 50 so round down
Find the slope of each line.
Answer:
Step-by-step explanation:
slope is rise over run or y over x
Let m be the slope
On this case, simply count the units for both x and y from tip to tip of the line segment
m = y/x
direction of the line is up and right so the sign is both positive
m = 4/1
m = 4
m = y/x
direction of the line is down and right so y is negative and x is positive
m = -3/4
The area of the trapezium, pqrs is
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!
To start, let's quickly review what a trapezium is. A trapezium, also known as a trapezoid, is a four-sided geometric shape with two parallel sides (called the bases) and two non-parallel sides (called the legs). The distance between the two parallel sides is known as the height.
In order to find the area of a trapezium, we use the formula:
Area = (sum of bases x height) / 2
So for trapezium PQRS, we need to identify the length of its two bases and its height in order to use this formula.
Without any specific measurements given in your question, I'll assume we don't have any numerical values to work with. Instead, let's use variables to represent the length of each base and the height.
We can call the shorter base PQ, and the longer base SR. Let's say PQ has a length of 'a' units, and SR has a length of 'b' units. For the height, let's call it h.
So, the formula for the area of trapezium PQRS becomes:
Area = ((a + b) x h) / 2
This means that to find the area of the trapezium, we simply need to know the lengths of the two bases (a and b) and the height (h).
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!
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According to the NCAA 7.1% of high school women cross country runners will end up running cross country at the collegiate level. If 30 female high school cross country runners are selected at random, what is the probability that exactly 2 of them will run cross country in college. Express your answer as a probability between 0 and 1 and round your answer to three decimal places.
Answer:
Step-by-step explanation:
5. Find the volume of the pyramid below? 4. Find the volume of the cone below.
40m
30m
52m
The volume of the rectangular pyramid is 20800 m³.
How to find the volume of a pyramid?The volume of the pyramid can be found as follows:
The pyramid is a rectangular base pyramid. Therefore,
volume of the pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore,
B = 52 × 30
B = 1560 m²
volume of the pyramid = 1 / 3 × 1560 × 40
volume of the pyramid = 62400 / 3
volume of the pyramid = 20800 m³
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HELP! NEED ANSWERS FAST
Answer:
BF×BA= DF×CF
9×2=3x
x = 6
AB=9
CD=11
Round 473,615 to the nearest hundred
Rounding 473,615 to the nearest hundred gives us 473,600.
We have,
Rounding a number to the nearest hundred means that you are looking at the digit in the tens place of the number.
If that digit is 5 or greater, you round up the digit in the hundreds place, and if it is less than 5, you keep the digit in the hundreds place the same.
In the case of 473,615, the digit in the tens place is 1, which is less than 5. So we keep the digit in the hundreds place (3) the same and round the remaining digits to zero.
Thus,
Rounding 473,615 to the nearest hundred gives us 473,600.
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in how many ways can first , second , and third prizes be awarded in a cont with 925 contestants? assume there is no ties
Answer:
Step-by-step explanation:
[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]
To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.
For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.
The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:
Number of ways = 925 * 924 * 923
Calculating this expression, we find:
Number of ways = 779,449,100
Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.
1) Use the figure to answer the
following question.
What is the volume of the following figure?
9 cubic units
10 cubic units
20 cubic units
1 cubic unit
Answer:
10
Step-by-step explanation:
If you multiply the width with the length and height , you will get nine, then add that lonely brick on top to get ten
What is the range of this data ?
60 65 70 75 80 85 90 95 100
Polygon PSRT is drawn with vertices at P(1, 5), S(1, 0), R(−2, −3), T(−4, 2). Determine the image vertices of P′ if the preimage is rotated 90° counterclockwise.
P′(1, 5)
P′(−1, −5)
P′(5, −1)
P′(−5, 1)
The image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).
To determine the image vertices of P' when the preimage is rotated 90° counterclockwise, we can use the following formula:
(x', y') = (-y, x)
where (x, y) are the coordinates of the preimage vertex, and (x', y') are the coordinates of the image vertex after rotation.
Using this formula for each vertex of the polygon PSRT, we get:
For P(1, 5), rotating 90° counterclockwise gives us P'(-5, 1).
For S(1, 0), rotating 90° counterclockwise gives us S'(0, -1).
For R(-2, -3), rotating 90° counterclockwise gives us R'(3, -2).
For T(-4, 2), rotating 90° counterclockwise gives us T'(-2, -4).
Therefore, the image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).
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The chemical element mercury has a melting point of -39. The melting point of bromine is -7. Which statement is an accurate comparison of these melting points?
From the given statements, the first statement which states, the melting point of mercury is 32 degrees cooler than the melting point of bromine is correct.
Given that, the melting point of mercury = -39
the melting point of bromine = -7
the difference between both melting points = -39 - (-7) = -32
In math, as we go to the negative values, the value of the number decreases. [-7 > -39]
From the above analysis, we can conclude that the melting point of mercury is 32 degrees cooler than the melting point of bromine. So, the option A which is the first statement is correct from the given image.
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Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.
What is the volume of a solid?The volume of a solid is the three dimensional space the solid occupies.
The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;
Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³
Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³
70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³
The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0
The number of times Johnny needs to use the wheelbarrow is about 41 times
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Which two statements about angles on a transversal crossing parallel lines contradict each other?
I. ∠1 and ∠2 are same-side interior angles.
II. m∠1 = m∠2
III. m∠1 + m∠2 = 90
The solution is: I. ∠1 and ∠2 are same-side interior angles and,
III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.
Here, we have,
given that,
We have to find which two statements about angles on a transversal crossing parallel lines contradict each other.
we know that,
If a transversal intersects or crosses parallel lines, adjacent angles are supplementary.
Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines.
now, we have,
I. ∠1 and ∠2 are same-side interior angles it can be possible.
Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.
Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary. If , then m ∠ 1 + m ∠ 2 = 180 ∘ .
so, if number-l is true, so, we get,
II. m∠1 = m∠2 may be true,
III. m∠1 + m∠2 = 90, never can be true.
so, we get,
if, l. holds then lll. contradicts that.
Hence, The solution is: I. ∠1 and ∠2 are same-side interior angles and,
III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.
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2 divided by blank equals 0.2
Answer:
10
Step-by-step explanation:
2 / 10 = 0.2
2 divided by ten is two-tenths.
Answer: 2 divided by 10 is 0.2
Find the quotient and remainder using synthetic division for
x^5
-
x^4
+
1
x^3
-
1
x^2
+
1
x
-
10
/x
-
1
The quotient is
The remainder is
The solution to the given problem of equation comes out to be quotient : x² +x+6+2/(x+2) and remainder is 2.
We have to find the remainder and quotient
Given : synthetic division for
x³ + 3x² + 8x + 14
------------------------
x + 2
Write the problem in synthetic division format
-2 | 1 3 8 14
-2 -2
------------------------
1 1 6
Carry down the leading coefficient, unchanged, to below the division symbol
-2 | 1 3 8 14
-2 -2
---------------------------
1 1 6
Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:
1(-2)=-2
-2 | 1 3 8 14
-2 - 2
------------------
1 1 6
=> We get:
As x² +x+6+ 2/(x+2)
and remainder is 2
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Gina puts $5500 into an account earning 5.25% interest compounded continuously how long will it take for the amount in the account to go to $7450
Using the formula of compound interest, the number of years is 7.6 years
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula of compound interest is given as;
[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]
A = Compounded InterestP = Principalr = raten = number of times compoundedt = number of years.But in this case, the interest was compounded continuously
[tex]A = Pe^r^t[/tex]
Substituting the values into the formula;
[tex]7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)[/tex]
Solving for t;
t = 7.6 years
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Daisy works at an ice cream parlor. She's paid $10/hr. For first 8hrs she works in a day for every extra hr she is paid 1.5x her hourly wage if daisy works x hours in a day and x is > 8 expression giving her net earnings for the day is _. If daisy works 13 hrs she is paid _
Daisy would be paid $155 if she works 13 hours in a day.
If Daisy works for up to 8 hours in a day, she is paid a flat rate of $10 per hour, so her earnings for the day would be:
Earnings = 10 × 8 = $8
If Daisy works for more than 8 hours in a day, then her earnings for the extra hours are calculated at a rate of 1.5 times her hourly wage, which is $15 per hour.
So, if Daisy works x hours in a day, where x is greater than 8, then her net earnings for the day can be expressed as:
Earnings = 80 + (x - 8) × 15
This expression takes into account the first 8 hours of work, which are paid at a flat rate of $10 per hour, and the extra hours, which are paid at a rate of $15 per hour
If Daisy works 13 hours in a day, then her net earnings for the day would be:
Earnings = 80 + (13 - 8) × 15 = 80 + 5 × 15 = $155
So Daisy would be paid $155 if she works 13 hours in a day.
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NO LINKS!! URGENT HELP PLEASE!!
What is the surface of this problem? Please show work!!
Answer:
720 m^2
Step-by-step explanation:
Solution:
The formula for the surface area of a triangular prism is:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S1 +S2 + S3)L + bh
where,
b is the bottom edge of the base triangle,h is the height of the base triangle,L is the length of the prism andS1, S2, and S3 are the three edges (sides) of the base triangle(bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bhGiven:
side 1 (S1) : 5 m
side 2(S2): x m
side 3(S3): 12 m
length (l)=22m
Here we need to find side 2, we can easily find it using Pythagoras' theorem.
a^2+b^2=c^2
5^2+12^2=x^2
x^2=169
x=[tex]\sqrt{169}=13 m[/tex]
therefore, side 2 is 13 m.
Substituting value in the formula
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S1 +S2 + S3)L + bh
Surface Area=(5+13+12)*22+5*12= 720 m^2
Answer:
720 m²
Step-by-step explanation:
The given diagram shows a triangular prism.
A triangular prism consists of two congruent triangular bases and three rectangular faces connecting these bases.
To calculate the surface area of the triangular prism, we first need to calculate the length of the hypotenuse of the right triangular base. To do this, we can use Pythagoras Theorem:
[tex]\begin{aligned}\sf Hypotenuse\;of\;triangular\;base&=\sqrt{5^2+12^2}\\&=\sqrt{25+144}\\&=\sqrt{169}\\&=13\; \sf m\end{aligned}[/tex]
The surface area of a triangular prism is the sum of the areas of all its faces. Therefore:
[tex]\begin{aligned}\sf Total\;surface\;area&=2\left(\dfrac{1}{2} \cdot 5 \cdot 12\right)+12\cdot 22+5 \cdot 22+13 \cdot 22\\\\&=60+264+110+286\\\\&=720\; \sf m^2\end{aligned}[/tex]
Therefore, the total surface area of the given triangular prism is 720 m².
NEED HELP ASAP!! WILL MARK BRAINLEST!!! PLS DONT GUESS IF YOU DONT KNOW!!
Answer:
it is A
Step-by-step explanation:
def correct! a+ student
Answer: D
Step-by-step explanation:
The answer has to be A or D because they're the only ones that look like real box-and-whisker plots. The mean is the line in the middle of the "box", so calculating the mean should be easy enough.
Add all the numbers together and then divided by the number of numbers.
56+72+75+98+73+86+48+95+69+88+75+92 = 972
There are 12 numbers.
972/12 = 77.25
Only option D represents the proper mean.
A popular Dilbert cartoon strip (popular among statisticians, anyway) shows an allegedly “random” number generator produces the sequence 999999 with the accompanying comment, “That’s the problem with randomness: you can never be sure.” Most people would agree that 999999 seems less “random” than, say, 703928, but in what sense is that true? Imagine we randomly generate a six-digit number, i.e., we make six draws with replacement from the digits 0 through 9. (a) What is the probability of generating 999999?
(b) What is the probability of generating 703928?
(c) What is the probability of generating a sequence of six identical digits?
(d) What is the probability of generating a sequence with no identical digits? (Comparing the answers to (c) and (d) gives some sense of why some sequences feel intuitively more random than others
.)
(e) Here's a real challenge: what is the probability of generating a sequence with exactly one repeated digit?
(a) the probability of generating 999999 is [tex](1/10)^6[/tex]
(b) the probability of generating 703928 is [tex](1/10)^6[/tex]
(c) the probability of generating a sequence of six identical digits is [tex](1/10)^6[/tex]
(d) the probability of generating a sequence with no identical digits is 15,120/1,000,000.
(e) the probability of generating a sequence with exactly one repeated digit is[tex]10 * 6 * (9^4).[/tex]
What is probability?Probability is described as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The probability of generating a sequence with no identical digits is calculated as (10/10) * (9/10) * (8/10) * (7/10) * (6/10) * (5/10) = 15,120/1,000,000.
We start by choosing the digit to be repeated, which can be done in 10 ways and the next thing is to choose the position of the repeated digit, and can be done in 6 ways.
We then see that remaining four positions can be filled out with any of the other 9 digits and this can also be done in [tex]9^4[/tex] ways.
So we can conclude that the number of possibilities in this case is [tex]10 * 6 * 9^4.[/tex]
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polar point : (6,3π).
Find three additional polar representations of the point, using −2 < < 2. (Enter your answers in order from smallest to largest first by r-value, then by -value.)
Find three additional polar representations of the point, using −2π<θ<2π. (Enter your answers in order from smallest to largest first by r-value, then by θ-value.) (r,θ)= ( (r,θ)r= ( (r,θ)= ( Question: That's it! Find three additional polar representations of the point, using −2π<θ<2π.
If the perimeter of the large square tile is 48 inches
and the perimeter of the smaller square is 16 inches,
what is the perimeter of one of the isosceles
trapezoids?
Answer: 27.3 inches
Step-by-step explanation:
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer: 29.9986-----30.0 degrees
Step-by-step explanation:
x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]
[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]
Which of the following table represents a linear function?
The table that represents a linear function is the second table.
Which of the tables represents a linear function?A linear function is written as:
y = ax + b
We can see that for each increase of 1 unit in the value of x, the value of y increases by a units.
Then we need to identify the table where the increases in the y-value are constant.
With that in mind we can discard options 1, 3 and 4.
Wher particularly options 1 and 4 show that sometimes the y-value increases and sometimes decreases, that is why we discard these.
Then the remainign option must be the correct one, which is the second option.
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What is the value of the y-intercept of the graph of h(x)=12.3(4.9)^x ?
Record your answer in the boxes below.
The value of the y-intercept of the graph of the function h(x) = 12.3(4.9)^x is 12.3.
To determine the value of the y-intercept of the graph of the function[tex]h(x) = 12.3(4.9)^x,[/tex] we need to find the value of h(0) since the y-intercept corresponds to the point where the graph intersects the y-axis (x = 0).
Substituting x = 0 into the function, we have:
[tex]h(0) = 12.3(4.9)^0[/tex]
Since any number raised to the power of 0 is equal to 1, we have:
h(0) = 12.3(1)
Multiplying 12.3 by 1 gives us:
h(0) = 12.3
Therefore, the value of the y-intercept of the graph of [tex]h(x) = 12.3(4.9)^x[/tex] is 12.
The y-intercept represents the value of the function when x = 0, which in this case is 12.3.
It is the point where the graph crosses the y-axis.
This means that when there is no exponential growth or decay (x = 0), the value of the function is 12.3. As x increases or decreases, the function will grow or decay exponentially, but at x = 0, it starts with a value of 12.3.
The graph of this function would start at the point (0, 12.3) and then either increase or decrease exponentially depending on the value of the base (4.9 in this case).
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given this equation, what is the value of y at the indicated point?
(6,y)
y^2 = x - 3
Please Help. am very stuck!
The value of y at the indicated point is √3.
What is a square root function?In Mathematics and Geometry, a square root function refers to a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In this scenario and exercise, we would determine the y-value by substituting the x-value into the given square root function as follows;
y² = x - 3
By taking the square root of both sides of the square root function, we have:
y = √(x - 3)
When x = 6, the y-value is given by;
y = √(6 - 3)
y = √3
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Tim brought $40.50 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Tim had $2.00 left over after buying these items.
What was the cost of each item?
Answer:
Let x be the cost of the pass.
Then the cost of the souvenir is (2/3)x.
The cost of the burger is (1/4) of the cost of the souvenir, which is (1/4)(2/3)x = (1/6)x.
The total cost of the items is x + (2/3)x + (1/6)x = (11/6)x.
Tim had $2.00 left over after buying these items, so we can set up the equation:
(11/6)x + 2 = 40.50
Solving for x, we get:
x = 18
Therefore, the cost of the pass is $18, the cost of the souvenir is (2/3)($18) = $12, and the cost of the burger is (1/6)($18) = $3.
A right triangle has a hypotenuse of 15 centimeters.
What are possible lengths for the two legs of the
triangle?
Answer:
Step-by-step explanation:
Since the given figure is a right triangle, we can use Pythagorean Theorem
where c² = a² + b²
c = 15
15² = a² + b²
Since 15 is the hypotenuse, we can then say that the possible legs of the triangle are less than 15.
225 - a² = b²
we will do trial and error
let a be 14
225 - 14² = b²
b = √29
a = 14cm, b = √29cm, c = 15cm
let a be 13
225 - 13² = b²
b = 2√14
a = 13cm, b = 2√14cm, c = 15cm
let a be 12
225 - 12² = b²
b = 9
a = 12cm, b = 9cm, c = 15cm
You can solve for other possible values using the same process as above. Since there are no conditions whether the lengths of the legs should be a whole number or not then the above dimensions can be considered. If you're looking for an answer that consists of whole numbers then the answer would be a = 12cm, b = 9cm and c = 15cm
Ms. Toney bought a rug for her classroom. The rug is 8 feet wide. The diagonal length of the rug is 14 feet. What would be the length of the rug she bought?
Answer:
11.49
Step-by-step explanation:
a^2+b^2=c^2
think of this as a triangle, we are going to use Pythagorean theorem.
the hypotenus is 14 ft and one of the legs is 8 ft. so the other leg is x
8^2 + x^2 = 14^2
64 + x^2 = 196
subtract the 64 on both sides
x^2 = 132
to counter the square we square root it
so x = the square root of 132 which comes out to a decimal
11.489....
rounded it would be 11.49
hope this helped
The table shows the net revenue in millions of dollars of a company every three months for two years. An exponential function can be used to model the data.
Company
Time, x (months) Net Revenue, r(x) (millions of dollars)
3 274
6 389
9 467
12 560
15 960
18 1,100
21 1,320
24 1,584
Which function best models the data?
r(x)=223.06(1.09)^x
r(x)=1.09(223.06)^x
r(x)=2,232.91(0.92)^x
r(x)=0.92(2,232.91)^x
An exponential function that best models the data include the following: A. [tex]r(x) = 223.06(1.09)^x[/tex]
How to determine the equation of line of best fit?In this scenario, the Company Time, x (months) would be plotted on the x-axis (x-coordinate) of the scatter plot while the Net Revenue, r(x (millions of dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the Company Time, x (months) and the Net Revenue, r(x (millions of dollars), an exponential equation for the line of best fit is given by:
[tex]r(x) = 223.06(1.09)^x[/tex]
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