The area of trapezoid is 47.5 cm².
What is trapezoid?A quadrilateral having only two sides parallel.The area of a trapezoid is the half of the product of sum of its parallel sides to the height of that trapezoid (the distance between those parallel sides).
Thus, if we have:
Length of its parallel sides = 'a' and 'b' units respectively
Perpendicular distance between its parallel sides = 'h' units,
Then, we get:
[tex]A = \dfrac{1}{2}\times(a+b) \times h \: \rm unit^2[/tex]
Given;
trapezoid has two bases that measure 11 cm and 8 cm.
a= 11 cm, b= 8 cm
Now, height= 5
A = (½* height) x (Sum of the bases)
A= 1/2 * ( 11 + 8) * 5
A= 95/2
Therefore, the Area trapezoid will be 47.5 cm²
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The complete question is;
A trapezoid has two bases that measure 11 cm and 8 cm. The height of the figure is 5 cm. What is the area of the trapezoid?
how many grams of an 80% solution and how many grams of a 54% solution do we have to mix in order to obtain 25 liters of a 42% solution
So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.
Mixing solution to obtain 42% solutionTo obtain 25 liters of a 42% solution, you would need to mix a certain amount of an 80% solution with a certain amount of a 54% solution. To determine the specific amounts, you would need to set up and solve a system of equations.
Let x be the amount of 80% solution in liters and y be the amount of 54% solution in liters. The total volume of the mixture is the sum of the volumes of the two solutions, so we have:x + y = 25
The percentage concentration of the mixture is the sum of the mass fractions of the solute in the two solutions, so we have:(0.8x) + (0.54y) = 0.42(x + y)
Solving this system of equations will give you the amount of each solution you need to use.x = (0.42*25) / (0.8 + 0.54) = 14.58 liters
y = 25 - x = 10.42 liters
So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.Learn more about Mixing solution to obtain 42% solution here:
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The populations of Siberian tigers and narwhals since 199019901990 are represented by the following tables
It is recommended to model the data in the tables using a ilnear or exponential function.
The exponential function will be the best model for tigers.
The optimal model for narwhals will be a linear function.
Test for vertical lines:
A vertical line test can be used to determine whether an expression is a function or not. In this test, we look for a single image of x and determine whether we receive one or many images.
It won't be a function if we receive more photographs.
For illustration, use y2 = 4ax.
y = ±√4ax
We receive two values of y for a single value of x.
Consequently, it won't be a function.
Due to that,
There are two data sets for the numbers of tigers and narwhals.
first gather tiger info,
Let's see if it satisfies the requirement for a linear function or not.
y = mx + c
x = 0, y = 1204
1204 = m0 + c
c = 1204
y = mx + 12-04
when y = 1050 and x = 3
1050 = 3m + 1205
m = -155/3
If a linear relationship exists,
Therefore, y should be 902 for x = 6.
However, is not the same as 902.
So, for this dataset exponential function will be best.
Similarly, we can check for the second dataset.
And it will satisfy the all the conditions of linear function.
So, for the Narwhals linear function is best model.
Complete question:
The populations of Siberian tigers and narwhals since 1990 are represented by the following tables:
Determine whether the data described in the tables is best modeled by a linear function or an exponential function.
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A toy factory makes toy bunnies.
Each toy bunny holds a carrot. A bunny's height, h(x)
is three times the length of the carrot, x.
2. Write an equation for the function h(x).
h(x) =
Answer: h(x) = 3x
Step-by-step explanation:
The height of a toy bunny, h(x), is directly proportional to the length of the carrot, x. The given information is that the height of the bunny is three times the length of the carrot. Therefore, the equation for the function h(x) would be the answer above.
Answer:
h(x) = 3x
I'm so cool w/ my fashionista lipstick! :D
Find the distance between the points ( – 18,11) and ( – 18, – 19).
Answer: 15.4
Step-by-step explanation: d= [tex]\sqrt{(-18)^{2} - 18^{2}) +((-19)^{2} - 11^{2})\\[/tex]
[tex]\sqrt{361 - 121}[/tex]
[tex]\sqrt{240}[/tex]
15.4
A dozen long stemmed roses cost $48 What is the cost per rose?
Answer:
$4
Step-by-step explanation:
Given;
Dozen long stemmed roses cost $48
Question:
What is the cost per rose?
Solve:
Based on the given, we can see that it states that a dozen long stemmed roses cost $48.
Knowing that - Dozen = 12
Since, we know that dozen equal 12. Hence, 12 long stemmed roses cost $48.
Now, divide the cost by the amount to find the cost per rose.
Thus,
48 ÷ 12 = 4.
Therefore, the cost per rose is $4.
RevyBreeze
nareh ave r.300. hi brother ureh ave r.220. how much money mut nareh gave hi brother o that both of them will have the ame amount of money
Nareh should give his brother $80. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.
Subtract the amount of money that Urch has from the amount of money that Nareh has:
300 - 220 = 80
Nareh should give his brother $80 so that both of them will have the same amount of money.
Nareh currently has $300 and Urch currently has $220, so Nareh should give Urch $80 in order to make them have the same amount of money. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.
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Write the equation of the line that passes through the points
(
−
3
,
−
8
)
(−3,−8) and
(
6
,
−
4
)
(6,−4). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-4 +8}{6 +3} \implies \cfrac{ 4 }{ 9 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ \cfrac{ 4 }{ 9 }}(x-\stackrel{x_1}{(-3)}) \implies y +8 = \cfrac{ 4 }{ 9 } ( x +3)[/tex]
Simplify the expression.
-2. 6f +0. 7f-14-9
- 2. 6f +0. 7f-14-9 =
(Simplify your answer. Use integers or decimals for any numbers in the expression. )
what’s the answer
The simplified form of expression -2.6f +0.7f - 14 - 9 is -1.9f - 23
We know that an expression is nothing but a mathematical statement that consists of at least two terms( variables or constants) along with one algebraic operation.
As we know simplifying an expression means rewriting the same expression in a compact manner with no like terms.
To simplify expressions, we combine all the like terms ; solve all the given brackets, if any.
In the simplified expression, we left with unlike terms which cannot be reduced further.
Consider an expression:
-2.6f +0.7f - 14 - 9
We simplify above expression.
-2.6f +0.7f - 14 - 9
= (-2.6 + 0.7)f - (14 + 9) .........(combine like terms)
= -1.9f - 23
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Lucy ha a trawberry lace that i 36cm long. She need piece 18mm long to decorate a cake
The length of the strawberry lace Lucy has is 36cm, and she needs a piece 18mm long for her cake decoration.
To calculate how many pieces of the strawberry lace she needs, we must convert the measurements from centimeters to millimeters.
We can do this by multiplying 36 centimeters by 100 to get the length of the lace in millimeters (36 cm x 100 = 3600 mm). We then divide this number by the length of the desired piece (3600 mm / 18 mm = 200). Therefore, Lucy needs 200 pieces of 18mm long strawberry lace to decorate her cake.
To summarize, the formula used to calculate the number of pieces Lucy needs is:
(Length of lace in millimeters) / (Length of desired piece in millimeters) = Number of pieces needed.
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RIGHT ANSWER GETS 15 POINTS
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Your answer:
Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;
60° + 70° + y = 180°
130° + y = 180°
y = 180° - 130°
y = 50°
Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.
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help asap. ninas garden is 4 1/5 meters long and 3/10 meters wide what is the area of ninas garden?
Answer:
1.26 meters
Step-by-step explanation:
A cheetah travels
90 feet in 7 seconds.
How fast is that?
??? feet per second
The speed of the cheetah based on the information provided is 12.85 feet per second.
How to calculate the speed of the cheetah?The speed of a body in movement can be expressed using different units such as:
kilometers per hour = km/hfeet per second= ft/smeter per minute = m/mBased on this, it is necessary to find how much distance the cheetah covers every second by dividing the distance given by the time given as it follows:
90 feet / 7 seconds=12.85 feet per secondTherefore, the speed of the cheetah is 12.85 feet per second
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-4t + 14 = -9t + 24
what value of t makes the equation true
Answer: t=2
Step-by-step explanation:
-4t+14= -9t+24
+9t =+9t
5t+14=24
-14=-14
5t=10
5t/5 10/5
t=2
How would you describe the plant's growth over 6 weeks?
Plant Growth
10
9
8
7
6
3
2
1
0
1 2
6
3 4 5
Weeks
can't be determined
decreasing
about the same
O increasing
The plant's growth over 6 weeks is described as the increasing of plant volume and/or mass with or without formation of new structures such as organs, tissues, cells or cell organelles.
The term volume in math is called as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we need to describe the plant's growth over 6 weeks.
As we know that the stages that plants go through are from seed to sprout, then through vegetative, budding, flowering, and ripening stages.
On the other hand the nutritional needs of people and plants change as they grow.
Then the main stages in the life cycle of a plant are seed germination, seedling formation, growth, development and differentiation leading to a mature plant, pollination and fertilizations and the formation of fruit and seeds.
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Tell whether each function is written in standard form. If not, rewrite it
in standard form.
1. y = 3x
2. 7-y = 5x + 11
Given a gla
3. -2(x+y)+9=1
Answer
1: 3x-y=0
2: 5x+y= -4
3: y=-x+4
Step-by-step explanation:
find the probability that a randomly selected bank has an overdraft fee greater than $25. (use decimal notation. give your answer to two decimal places.
Answer:
Step-by-step explanation:
a survey for kindergartners asked about their favorite color. the children were asked to check the box corresponding to blue, red, green, yellow, or orange. what is the scale of measurement for this question? group of answer choices ordinal interval nominal ratio
Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.
Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.
Ratio scales are interval scales where lengths are expressed in relation to a rational zero.
Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.
Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.
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mr. brown went grocery shopping to buy meat for his annual office picnic. he bought 7 3 4 pounds of hamburger, 17.85 pounds of chicken, and 6 1 2 pounds of steak. how many pounds of meat did mr. brown buy?
There are 32.1 pounds of meat.
Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. The addition symbol is one of the widely used math symbols. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+). The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left.
Add up the pounds of meat.
7.75 + 17.85 + 6.5 = 32.1 pounds
Thus, there are 32.1 pounds of meat.
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If α and β are the zero of the quadratic polynomial p(x)=4x 2 −5x−1, find the value of α 2 ββ2 α
The value of α2ββ2α2 is -20. a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation.
Given,
p(x) = 4x2 − 5x − 1
α and β are the zeroes of the quadratic polynomial p(x).
Therefore,
α + β = -5/4
and
αβ = 1/4
Therefore,
α2ββ2α2 = (α+β)2αβ = (-5/4)2(1/4) = (-5/4)(-5/4)(1/4) = 25/16 = -20
Given a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation. To find the value of α2ββ2α2, we first need to find the sum and product of the two zeroes, which can be done by solving the equation. The sum of the zeroes is -5/4 and their product is 1/4. We can then use these values to calculate the value of α2ββ2α2, which is equal to (-5/4)2(1/4) = 25/16 = -20. Thus, the value of α2ββ2α2 is -20.
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Cost of carpeting a floor 2.50 per square feet how much will it cost to carpet a rectangular floor 10 feet by 12 feet
On a certain hot summer's day, 544 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $964.00. How
many children and how many adults swam at the public pool that day?
Answer:
248 children
296 adults
Step-by-step explanation:
Define the variables:
Let x = number of children using the public pool.Let y = number of adults using the public pool.Given information:
A total of 544 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totalled $964.00.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}\;\;\;\;\:\:\:x+y=544\\1.5x+2y=964\end{cases}[/tex]
Rearrange the first equation to isolate x:
[tex]\implies x=544-y[/tex]
Substitute the found expression for x into the second equation and solve for y:
[tex]\implies 1.5(544-y)+2y=964[/tex]
[tex]\implies 816-1.5y+2y=964[/tex]
[tex]\implies 816+0.5y=964[/tex]
[tex]\implies 0.5y=148[/tex]
[tex]\implies y=296[/tex]
Therefore, 296 adults swam at the public pool.
Substitute the found value of y into the equation for x and solve for x:
[tex]\implies x=544-296[/tex]
[tex]\implies y=248[/tex]
Therefore, 248 children swam at the public pool.
in a school of 330 students,85 of them are in the drama club 200 of them are in a sports team and 60 students do drama and sports
Answer: There would be 345 students because 85+200+60=345
Step-by-step explanation: it equal 245
Write an equivalent expression to 9 1/2k - (7 + 31/4k) without parentheses. Then, combine like terms
An equivalent expression to 9 1/2k - (7 + 31/4k) is 51k/4 +7
How to find the equivalent fraction?The given expression is 9 1/2k - (7 + 31/4k)
This involves the the simplification of the fraction above following the rule of BOADMAS
⇒19k/2 - 7/1 + 13k/4
Simplifying the right hand side of the fraction with parenthesis,
18k/2 - [(28+13k)/4
This fraction gives
*38k - 28+ 13k)/4
Collecting the like terms
= 25k + 28
Therefore the equivalent expression is 25k/1 + 7
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You borrowed $95 for 1 year at 5. 2% interest that is compounded semi annually. What will you pay back in full
You will pay back $100.00
We know that the formula for the compound ineterst:
[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]
where, A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
n = number of compounding periods
t = time in years
First, convert R as a percent to r as a decimal
r = 5.2/100
r = 0.052 rate per year,
Now we solve the equation for A
[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]
[tex]A = 95\times (1 +\frac{0.052}{2})^{2\times 1}[/tex]
A = 95.00 × (1 + 0.026)²
A = 100.004
A ≈ 100
Therefore, the total amount accrued with compound interest on a principal of $95.00 at a rate of 5.2% per year compounded semi annually is $100.00.
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Find the coordinates of the vertices after a 90 rotation about the origin and about each of the points L, M, and N
After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-3, -6) and (3, -4). Therefore, option D is the correct answer.
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
Given that, triangle LMN with vertices L(2, -2), M(6, -3) and N(4, 3).
After clockwise rotation 90° we get
Here, L(2, -2) →L'(-2, -2)
M(6, -3) →M'(-3, -6)
N(4, 3) →N'(3, -4)
Therefore, option D is the correct answer.
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Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours. He begins with a sample of the isotope with a mass of 92 grams. He then measures the mass of the object every hour. What is the approximate mass of the sample after 20 hours?
As per the given half life the approximate mass of the sample after 20 hours is 0.03125
The term half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
Here we have know that Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours.
And here we also know that he begins with a sample of the isotope with a mass of 92 grams and then measures the mass of the object every hour.
Then the approximate mass of the sample after 20 hours is calculated as,
=> 20/4 = 5
Then the value after 5 hours of time is calculated as,
=> 1/2⁵
=> 0.03125
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Liquid A and liquid B are mixed together in the ratio 4:11 by volume to make
liquid C.
Liquid A has density 1. 05g/cm
Liquid B has density 1. 27 g/cm
A cylindrical container is filled completely with liquid C.
The cylinder has radius 5 cm and height 20 cm.
Work out the mass, in g, of the liquid in the container.
Give your answer correct to 3 significant figures.
The mass of the liquid in the container is 18.17 g, correct to 3 significant figures
Calculate the volume of the container:
Volume = πr2h
Volume = π x (5 cm)2 x 20 cm
Volume = 3,142 cm3
Calculate the total volume of liquid A and B:
Total volume of A and B = 4:11
Total volume of A and B = 4 + 11 = 15 cm3
Calculate the volume of liquid A:
Volume of A = 4/15 x 15 cm3
Volume of A = 4 cm3
Calculate the volume of liquid B:
Volume of B = 11/15 x 15 cm3
Volume of B = 11 cm3
Calculate the mass of liquid A:
Mass of A = Volume of A x Density of A
Mass of A = 4 cm3 x 1.05 g/cm3
Mass of A = 4.2 g
Calculate the mass of liquid B:
Mass of B = Volume of B x Density of B
Mass of B = 11 cm3 x 1.27 g/cm3
Mass of B = 13.97 g
Calculate the total mass of liquid C:
Total mass of C = Mass of A + Mass of B
Total mass of C = 4.2 g + 13.97 g
Total mass of C = 18.17 g
The mass of the liquid in the container is 18.17 g, correct to 3 significant figures.
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Solve each trigonometric function IN THE INTERVAL [0, 2).
sin(x) + 1 = cos(x)
The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The trigonometric function is given below.
sin(x) + 1 = cos(x)
Simplify the equation, then we have
sin(x) + 1 = cos(x)
(sin(x) + 1)² = cos² (x)
(sin(x) + 1)² = 1 - sin² (x)
sin² (x) + 2sin x + 1 = 1 - sin² (x)
2sin² (x) = 0
sin (x) = sin 0
x = 0
The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.
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identify the number as real, complex, pure imaginary, or nonreal complex. (more than one of these descriptions may apply)
-5
Answer:
real
Step-by-step explanation:
-5 is real. It is not complex because it is not in the form a+bi. It also has no imaginary part so it is neither of the other two.
Hope that helps, let me know if you have any other questions!
43% of all statistics classes require a statistical calculator and 27% require the use of a computer that has statistical software. Of the classes that require a statistical calculator, 17% also require the use of a computer. If a statistics course is selected at random find: (round to 4 decimal places where possible)
The probabilities of the events are
a. 0.43
b. 0.27
c. 0.1161
d. 0.2444.
According to the question,
Statistics classes require a statistical calculator = 43% = 0.43
Statistics classes require a computer that has statistical software = 27% = 0.27
Of the classes that require a statistical calculator, classes also require the use of a computer = 17% = 0.17
a. P(Statistical Calculator)
= 0.43
b. P(Statistical Software)
= 0.27
c. P(Require a Statistical Calculator and Statistical Software)
⇒ (0.43)(0.27)
= 0.1161
d. P(Require a Statistical Calculator GIVEN Require Statistical Software)
⇒ 0.066/0.27
⇒ 0.2444
Hence we can conclude that the probabilities of the events are
a. 0.43
b. 0.27
c. 0.1161
d. 0.2444
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