The solution to the system of equations is p = 4 and q = 2
What do you mean by Substitution method ?The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.
To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:
p + 2q = 8
p = 8 - 2q
Now we can substitute this expression for p in the first equation:
2p - 3q = 2
2(8 - 2q) - 3q = 2
16 - 4q - 3q = 2
16 - 7q = 2
-7q = -14
q = 2
We can now substitute q = 2 into the expression we found for p:
p = 8 - 2q
p = 8 - 2(2)
p = 4
Therefore, the solution to the system of equations is p = 4 and q = 2.
correct question Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.
Learn more about Substitution method here
https://brainly.com/question/14619835
#SPJ1
the empirical rule assumes that the distribution of data follows a normal curve. group startstrue or false
The statement "The empirical rule assumes that the distribution of data follows a normal curve." is True.
The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This implies that the distribution of data follows a normal curve.
A normal distribution is a type of probability distribution that follows a symmetrical bell-shaped curve. It is also known as the Gaussian distribution and is a continuous probability distribution. The normal distribution is defined by its mean, which is the average of the values, and its standard deviation, which is a measure of the spread of the values from the mean.
To learn more about empirical rule link is here
brainly.com/question/30700783
#SPJ4
It starts to snow at 10:54 AM it snows for two hours 16 minutes without stopping what time does a snow stop ?
Please help with this problem
To arrive at this answer, you can add the duration of the snowfall to the starting time to get time 1:10 PM
what is duration?
Duration refers to the length of time that something lasts or continues. It is the amount of time between the start and end of an event or activity. For example, the duration of a movie could be two hours, the duration of a concert could be three hours,
In the given question,
If it starts snowing at 10:54 AM and it snows for two hours and 16 minutes without stopping, then the snow will stop at 1:10 PM.
To arrive at this answer, you can add the duration of the snowfall to the starting time.
10:54 AM + 2 hours 16 minutes = 1:10 PM
To know more about duration, visit:
https://brainly.com/question/29974796
#SPJ1
Harper is working two summer jobs, making $12 per hour babysitting and $8 per hour landscaping. Harper must earn no less than $140 this week. Write an inequality that would represent the possible values for the number of hours babysitting, b b, and the number of hours landscaping, l l, that Harper can work in a given week.
The inequality that represents the possible values for the number of hours babysitting and the number of hours landscaping is 12b + 8l ≥ 140.
What is Inequality:A mathematical inequality is a statement that two quantities or expressions are not equal. Inequalities are used to compare the relative sizes of numbers or variables and represent constraints or conditions in various contexts, such as optimization problems, systems of linear equations, or financial planning.
Here we have
Harper is working two summer jobs, making $12 per hour babysitting and $8 per hour landscaping. Harper must earn no less than $140 this week.
Let Harper work for 'b' hours in the baby setting and l hours in landscaping
The amount earned by Haper by babysitting = $ 12 × b = 12b
The amount earned by Haper by landscaping = $ 8 × l = 8l
Here the amount should not be less than $ 140
=> 12b + 8l ≥ 140
Hence,
The inequality that represents the possible values for the number of hours babysitting and the number of hours landscaping is 12b + 8l ≥ 140.
Learn more about Inequality at
https://brainly.com/question/29413699
#SPJ1
what is the equation of a rational function that has a x-intercept at (6,0), vertical asymptote at x=-3, and horizontal asymptote at y=-1
[tex]f(x) = (2/3)(x - 6)/(x + 3)[/tex]
Complete the statement. In any given circle, the measure of a(n) Choose... is one-half the measure of the Choose..
Answer:
In any given circle, the measure of an inscribed angle is one-half the measure of the central angle that intercepts the same arc.
PLEASE HELP ILL GIVE BRAINLIEST
Answer: 1 and 5
Step-by-step explanation:
Find the midpoint of the line segment with end coordinates of:
(−2,−4) and (−1,−5)
Give coordinates as decimals where appropriate.
What is the answer
Answer:
(- 1.5, - 4.5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 2, - 4 ) and (x₂, y₂ ) = (- 1, - 5 ) , then
midpoint = ( [tex]\frac{-2-1}{2}[/tex] , [tex]\frac{-4-5}{2}[/tex] ) = ( [tex]\frac{-3}{2}[/tex] , [tex]\frac{-9}{2}[/tex] ) = (- 1.5, - 4.5 )
what fraction of 5 litres is 6800ml give answer as mixed number and lowest term
The fraction of 5 liters that is 6,800 ml is 8/5 or 1 3/5 in mixed number form, which represents one whole 5-liter container plus 3/5 of another 5-liter container.6800 ml is equivalent to 6.8 liters. To find the fraction of 5 liters that is 6.8 liters, we can divide 6.8 by 5:
6.8 / 5 = 1 3/5
Therefore, the fraction of 5 liters which is 6800 ml is 1 3/5, which is a mixed number. This means that the total volume of 6.8 liters is equivalent to one whole 5-liter container, plus 3/5 of another 5-liter container.
To convert this mixed number into a fraction, we can first multiply the whole number by the denominator of the fraction and add the numerator to get the improper fraction:
1 * 5 + 3 = 8
The improper fraction is 8/5. This means that 6.8 liters are equivalent to 8/5 of 5 liters.
To reduce the fraction to the lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 1:
8/5 = 8 ÷ 1 / 5 ÷ 1 = 8/5
A fraction is a mathematical representation of a part of a whole. It is written in the form of a numerator and a denominator separated by a horizontal line, where the numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole.
For example, the fraction 3/4 represents three parts out of a total of four parts. It can also be represented visually using a diagram such as a pie chart or a number line.
Fractions can be added, subtracted, multiplied, and divided, and can also be converted between different forms, such as mixed numbers, improper fractions, and decimals. They are commonly used in a variety of mathematical applications, such as in measurements, ratios, and proportions, as well as in everyday life situations, such as dividing a pizza into slices or calculating discounts on a sale.
Find out more about fraction
brainly.com/question/17122642
#SPJ4
how do you multiply 7(b-5)(b-4) step by step
To multiply 7(b-5)(b-4), you can follow these steps:
1.
Start by distributing the 7 to the terms inside the parentheses:
7(b-5)(b-4) = 7 * b * (b-4) - 7 * 5 * (b-4)
2.
Simplify each term using the distributive property:
= 7b^2 - 28b - 35b + 140
3.
Combine like terms:
= 7b^2 - 63b + 140
So, the final answer is 7b^2 - 63b + 140.
I need helppppppppppppppppp
Answer:
Step-by-step explanation:
You just need to finish your proof by
adding what you were intending to prove.
m∠ ABC is equal to the m∠GHI.
You are correct so far.
A potato manufacturer make a small bag that holds 2 pounds of potatoes. They want to make a bag for Costco that holds 20 pounds of potatoes. By approximately what factor will the surface area of the bag increase? Round to the nearest tenth.
factor:
The surface area of the larger bag will increase by a factor of approximately 10.
What is surface area?
The surface area of a three-dimensional object is the total area of all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things. increase.
In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.
This is because the surface area of a three-dimensional object is proportional to the square of its linear dimensions.
Since the linear dimensions of the larger bag are 10 times that of the smaller bag (20 pounds vs. 2 pounds), the surface area of the larger bag will be roughly [tex]10^{2 }= 100[/tex] times that of the smaller bag.
To know more about the object visit: https://brainly.com/question/14964361
#SPJ1
suppose your friends have the following ice cream flavor preferences: 70% of your friends like chocolate (c). the remaining do not like chocolate. 40% of your friends like sprinkles (s) topping. the remaining do not like sprinkles. 25% of your friends who like chocolate (c) also like sprinkles (s). of the friends who like sprinkles, what proportion of this group likes chocolate? (note: some answers are rounded to two decimal places.)
We can start by creating a table to organize the information:
Likes Chocolate (c) Does Not Like Chocolate (~c) Total
Likes Sprinkles (s) 0.25 0.40
Does Not Like Sprinkles (~s) 0.60
Total 0.70 0.30 1.00
We are given that 40% of friends like sprinkles, so we can fill in that cell of the table. We are also given that 25% of friends who like chocolate also like sprinkles, so we can fill in the cell for likes chocolate and likes sprinkles as 0.25.
To find the proportion of friends who like sprinkles and chocolate, we need to divide the number of friends who like both by the total number of friends who like sprinkles:
proportion = likes chocolate and sprinkles / likes sprinkles
proportion = 0.25 / 0.40
proportion = 0.625
So, approximately 62.5% of friends who like sprinkles also like chocolate.
←
What is the total cost of a $704 tablet computer that is on sale at 13% off if the local sales tax rate is 4%?
The total cost of the tablet is S
(Round to two decimal places as needed.)
Answer:
636.98
Step-by-step explanation:
[tex]704 * .13 = 91.52 (discount)\\704 - 91.52 = 612.48 (price after discount)\\612.48 * .04 = 24.4992 (tax)\\612.48 + 24.4992 = 636.9792(Price with tax)\\round= 636.98[/tex]
the sales tax applies to the price after the discount is applied
write the opposite of -4 1/2 and explain how it's related to -4 1/2. Use a number line as a reference in your explanation. Use the number line to think about the location of the number 2 and the number n, where n is greater than 3. write an inequality comparing the opposite of 2 and the opposite of n. explain how the number line shows that your inequality is correct
We can use the number line to see that 2 and any number greater than 3 are to the right of -4 1/2. By finding the Opposites of 2 and n and comparing them, we can write an inequality that is correct based on the number line.
The opposite of -4 1/2 is 4 1/2. This is because the opposite of a number is the number that is the same distance from 0 on the number line, but in the opposite direction. On a number line, -4 1/2 is to the left of 0, so its opposite, 4 1/2, is to the right of 0.
Looking at the number line, we can see that the number 2 is to the right of -4 1/2, but to the left of 4 1/2. Any number greater than 3, represented by n, is also to the right of -4 1/2.
The opposite of 2 is -2 and the opposite of n is -n. So, the inequality we can write is:
-n < -2
This is because -2 is to the left of -n on the number line. We can see that this inequality is correct on the number line because -2 is closer to 0 than -n, which means that -n is less than -2.
In summary, the opposite of -4 1/2 is 4 1/2, and it is related to -4 1/2 because they are the same distance from 0 on the number line, but in opposite directions. We can use the number line to see that 2 and any number greater than 3 are to the right of -4 1/2. By finding the opposites of 2 and n and comparing them, we can write an inequality that is correct based on the number line.
To Learn More About Opposites
https://brainly.com/question/22882212
SPJ11
The remainders obtained when px³ + qx² + 4x − 2 is divided by x-1 and x + 2 are
equal. Show that 3p - q = -4. If also the remainder is -18 when the polynomial is
divided by x-2, find the value of p and of q.
Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.
what is polynomial ?A polynomial is a mathematical equation composed of variables and coefficients that is solved using mathematical operations like combination, deletion, multiplication, and quel integer exponents.
given
The result of dividing the same polynomial by x + 2 is
(p[tex]x^{2}[/tex] + (2p-q)x + (5q-2))(x+2) + (q[tex]x^{3}[/tex] + q[tex]x^{2}[/tex]+ 4[tex]x^{2}[/tex]) (12p-9q-2)
p+2q-2 = 12p-9q-2
When we simplify this equation, we obtain:
11p + 2q = 0
=> 3p - q = -4 (by adding 22p to both sides and multiplying both sides by 2)
Now, we also understand that the polynomial, when divided by x – 2, leaves a remainder of -18. Synthetic division or polynomial long division yields the following results:
= (p (x-2)³ + (7p-2q)(x-2) (x-2)² + (18q-8p)(x-2)) - 18
When we compare coefficients, we find:
p = 7p - 2q = 18q - 8p = 0
Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.
To know more about polynomials visit:
brainly.com/question/11536910
#SPJ9
4. Given the following: X(7, 0), Y(7, 5) and Z(0, 5), calculate the distance or
length of XY, YZ, and XZ. What is the perimeter of the triangle?
a. 6.8 units
b. 11.3 units
c. 15.8 units
d. 20.6 units
Answer:
To calculate the distance or length of XY, YZ, and XZ, we can use the distance formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2] For XY: Distance = √[(7 - 7)^2 + (5 - 0)^2] Distance = √[0 + 25] Distance = √25 Distance = 5 units For YZ: Distance = √[(0 - 7)^2 + (5 - 5)^2] Distance = √[49 + 0] Distance = √49 Distance = 7 units For XZ: Distance = √[(0 - 7)^2 + (5 - 0)^2] Distance = √[49 + 25] Distance = √74 Therefore, the length
Write an equation tomorrow, the statement, the product of -8 and (y+3) is 32. How you can use the equation to reason about the value of Y?
The equation to model the statement is [tex]-8(y + 3) = 32[/tex] and the value of y is -7.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given statement is the product of – 8 and [tex](y + 3)[/tex] is 32.
Product means the operation is multiplication.
So the equation can be written as,
[tex]-8 (y + 3) = 32[/tex]
Dividing both sides by 8,
[tex]-(y + 3) = 4[/tex]
[tex]y + 3 = -4[/tex]
[tex]y = -4 - 3 = -7[/tex]
Hence the value of y is -7.
Learn more about Solving Equations here:
https://brainly.com/question/29050831
Determine whether the graph of the equation is symmetric with respect to the
The graph of the equation y = x² + 5 is symmetric with respect to the y-axis, the correct option is (b).
To determine the symmetry of the graph, we can substitute (-x) for x in the equation and simplify:
y = (-x)² + 5
y = x² + 5
Since the equation is unchanged when x is replaced by (-x), the graph is symmetric with respect to the y-axis.
We can also see that the graph is not symmetric with respect to the x-axis or the origin. To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the equation:
(-y) = x² + 5
y = -(x² + 5)
The equation is not the same as the original equation, so the graph is not symmetric with respect to the x-axis. Similarly, to check for symmetry with respect to the origin, we can substitute (-x) and (-y) for x and y in the equation:
(-y) = (-x)² + 5
y = x² + 5
The equation is not the same as the original equation, so the graph is not symmetric with respect to the origin.
To learn more about graph follow the link:
https://brainly.com/question/17267403
#SPJ1
The complete question is:
Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these
y = x² + 5
Check all the answers
a. The graph is symmetric with respect to the x-axis
b. The graph is symmetric with respect to the y-axis
c. The graph is symmetric with respect to the origin
d. none of the above
Question 3
A circular garden has
Round to the nearest
a circumference of 39.25 feet. Find the approximate diameter of the garden. Use 3.14 for T.
hundredth if necessary.
ft
Answer:
Sure! To find the diameter of the garden, we can use the formula: circumference = π x diameter Given that the circumference of the garden is 39.25 feet and π is approximately 3.14, we can plug in the values and solve for diameter: 39.25 = 3.14 x diameter diameter = 39.25 ÷ 3.14 diameter ≈ 12.5 feet (rounded to the nearest hundredth) Therefore, the approximate diameter of the garden is 12.5 feet.
a box next to the register at tacos and stuff, where cooper works, is filled with different-flavored sauce packets. when a customer asks for some spicy sauce packets, cooper reaches into the box and pulls out a large handful of packets, looking for the spicy ones. here are the flavors he pulls out: mild, mild, spicy, medium, spicy, mild, spicy, super-hot, mild, spicy, super-hot, mild, mild based on the data, what is the probability that the next packet cooper pulls out of the box will be spicy?
Based on the given data, there are a total of 13 packets and 5 of them are spicy. Therefore, the probability that the next packet Cooper pulls out of the box will be spicy is 5/13 or approximately 0.385 (rounded to three decimal places).
To calculate the probability of the next packet being spicy, we need to know how many packets of each flavor are in the box. Assuming that Cooper doesn't put back the packets he has pulled out, we can count the number of spicy packets and divide it by the total number of packets he pulled out.
In this case, out of the 13 packets he pulled out, 5 were spicy. Therefore, the probability of the next packet being spicy is 5/13, or approximately 0.38, or 38%. However, if the box is refilled with packets of different flavors, this probability may not hold.
To know more about Probability:
https://brainly.com/question/11234923
#SPJ4
Answer: 4/13
Step-by-step explanation: i did this IXL and this was the correct answer
Problems 13 & 14. Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement.
The triangles ABE and CED are similar in figure 1 by SAS similarity criteria whereas in figure 2 the triangles PST and RPQ are not similar.
What is similar triangle?The triangles are similar if all angles in one triangle are congruent to corresponding angles in other triangle and sides are proportional. There are different criterias for similarity of triangles namely SSS, SAS, ASA/AAS and RHS. According to the criteria/rule
SSS(SIDE-SIDE-SIDE):triangles are similar, if all three sides of one triangle are proportional to the three sides of another triangle.
SAS(SIDE-ANGLE-SIDE):The b are similar if two sides are proportional and an angle included is congruent to two sides and included angle of another triangle.
ASA(ANGLE-SIDE-ANGLE):The triangles are similar if two angles are equal and an side between the angles is proportional to the two angles and side between the angles of another triangle.
Q13) Consider ΔABE and ΔCED ,
∠AEB = ∠CED = 90°
and,
AE=21 units ;BE= 26+16=42 units
CE=16 units ; ED=32 units
and
∴ Sides are proportional
Hence ΔABE is similar to ΔCDE by SAS criteria.
Q14)Consider triangles ΔPQR and ΔPST,
Given that ∠QPT=42°, and PR bisects ∠QPT
∴∠QPR=∠RPT=21°
Given that ∠PTS=102°,
In ΔPST, by angle sum property of triangle:
∠SPT+∠PTS+∠TSP=180°
21 + 102 + ∠TSP=180°
∠TSP=180° - 102 -21
∠TSP=57°
Given that ∠PRQ=58°
In ΔPRQ, by angle sum property of triangle:
∠RPQ+∠QRP+∠PQR=180°
21 + 58 + ∠PQR=180°
∠PQR=180°- 58 - 21
∠PQR=101°
In ΔPRQ the three angles are 21°,101° and 58° whereas in ΔPST the three angles are 21°,102° and 57°. As the angles are not congruent, the triangles are not similar.
To know more about similar triangle visit:
https://brainly.com/question/14285697
#SPJ1
!!PLEASE HELPPP!! CHECK IF IM RIGHTTT
Answer:
You are correct
Step-by-step explanation:
in a randomized controlled trial, sometimes patients agree to receive an intervention but later decide to stop taking the medication. moreover, some patients who were assigned to placebo decide to stop taking the placebo pill and buy the drug on their own (even when they do not know that they are taking a placebo pill). when this happens, researchers typically do the analysis according to the original assignment of the treatment regardless of the actual treatment received. what is the name of this procedure to analyze the data?
The procedure used to analyze the given data is intention-to-treat analysis.
The procedure to analyze data according to the original assignment of the treatment regardless of the actual treatment received is called the intention-to-treat (ITT) analysis. It is considered the gold standard in clinical trial analysis because it preserves the randomization and avoids bias that may arise from differential dropouts or non-compliance. By analyzing all patients according to their randomized group, the ITT analysis provides an unbiased estimate of the treatment effect and better reflects the real-world effectiveness of the intervention.
The intention-to-treat (ITT) analysis is different from other types of analyses because it includes all patients according to their original randomized group, regardless of whether they received the assigned treatment or not. This is in contrast to per-protocol analysis, where only patients who completed the study without any major protocol deviations are included, or as-treated analysis, where patients are analyzed according to the actual treatment received.
Learn more about intention-to-treat analysis;
https://brainly.com/question/28297324
#SPJ4
Justin ate 1/2 of a pizza and Dan ate 3/8th. In total, how much pizza did they eat?
Answer: They ate 7/8 of the pizza in total.
find the value of w.
Answer:
w = 8
Step-by-step explanation:
[tex] \frac{24}{w + 4} = \frac{w + 4}{6} [/tex]
[tex] {(w + 4)}^{2} = 144[/tex]
[tex]w + 4 = 12[/tex]
[tex]w = 8[/tex]
You estimate that it requires fifty minutes to serve 85 customers through a cafeteria line. If your normal lunch crowd averages 200 customers, about how much time will it take for the lunch crowd to go through the cafeteria line (assuming a constant flow of customers)? To the nearest minutes
Answer:
If 85 customers can be served in 50 minutes, then we can find the number of minutes per customer by dividing 50 by 85: 50 minutes / 85 customers ≈ 0.588 minutes per customer To estimate the time required for 200 customers, we can multiply the time per customer by the number of customers: 0.588 minutes per customer x 200 customers ≈ 117.6 minutes Rounding to the nearest minute, we can estimate that it will take about 118 minutes for the lunch crowd of 200 customers to go through the cafeteria line.
The vertices of a rhombus are located at the coordinates (1, 3), (4, 7), (9, 7),
and (6, 3)
Find the length of the horizontal sides of the rhombus and its perimeter.
Answer: To find the length of the horizontal sides of the rhombus, we need to find the distance between points (1, 3) and (9, 7), which is the same as the distance between points (4, 7) and (6, 3).
Using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(9 - 1)² + (7 - 3)²]
d = √[64 + 16]
d = √80
d ≈ 8.94
So the length of the horizontal sides of the rhombus is approximately 8.94 units.
To find the perimeter of the rhombus, we need to find the distance between all four vertices and add them up.
Using the distance formula:
d₁ = √[(4 - 1)² + (7 - 3)²] = √25 = 5
d₂ = √[(9 - 4)² + (7 - 7)²] = √25 = 5
d₃ = √[(6 - 9)² + (3 - 7)²] = √16 + 16 = √32 ≈ 5.66
d₄ = √[(1 - 6)² + (3 - 7)²] = √25 + 16 = √41 ≈ 6.40
Perimeter = d₁ + d₂ + d₃ + d₄ = 5 + 5 + 5.66 + 6.40 ≈ 22.06
So the perimeter of the rhombus is approximately 22.06 units.
Step-by-step explanation:
Travis has the following books on his shelf: 6 myster, 5 science, 4 history, and 3 adventure. Travis will randomly choose 1 book to read. What is the probability (in fraction form) that he will choose a mystery book?
Answer: The probability that Travis will choose a mystery book is 1/3.
Step-by-step explanation: To find the probability that Travis will choose a mystery book, we need to determine the ratio of the number of mystery books to the total number of books on Travis's shelf.
Travis has 6 mystery books, and the total number of books on his shelf is 6 + 5 + 4 + 3 = 18.
Therefore, the probability (in fraction form) that Travis will choose a mystery book is 6/18.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 6.
6 ÷ 6 = 1
18 ÷ 6 = 3
So, the simplified fraction is 1/3.
please help!!! due tomorrow
(1 and 3 done)
The volumes of the figures are 728 cubic meters, 47.14 cubic yards, 1260 cubic centimeters, 5581.71 cubic inches and 860.07 cubic inches
Calculating the volumes of the figuresFigure 1:
The volume is calculated as
Volume = Product of dimensions/3
So, we have
Volume = 13 * 8 * 21/3
Volume = 728 cubic meters
Figure 2:
The volume is calculated as
Volume = πr²h
So, we have
Volume = 22/7 * 5² * 3/5
Volume = 47.14 cubic yards
Figure 3:
The volume is calculated as
Volume = Product of dimensions
So, we have
Volume = 14 * 18 * 5
Volume = 1260 cubic centimeters
Figure 4:
The volume is calculated as
Volume = 1/3πr²h
So, we have
Volume = 1/3 * 22/7 * 12² * 37
Volume = 5581.71 cubic inches
Figure 5:
The volume is calculated as
Volume = 1/3h(a² + b²)
So, we have
Volume = 1/3 * 13.3 * (16 * 6 + 14 * 7)
Volume = 860.07 cubic inches
Other dimensions are not clear
Read more about volumes at
https://brainly.com/question/463363
#SPJ1
Nicole is 1.55 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 30.05 meters. She stands 25.6 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
approximately 1.81 meters.
Step-by-step explanation:
Let's call the height of the tree "h". We can set up a proportion based on the similar triangles formed by Nicole, her shadow, the tree, and the tree's shadow:
(height of Nicole) / (length of Nicole's shadow) = (height of tree) / (length of tree's shadow)
Substituting the given values, we get:
1.55 / 25.6 = h / 30.05
Simplifying and solving for h, we get:
h = (1.55 / 25.6) * 30.05
= 1.81181640625
Rounding to the nearest hundredth, we get:
h ≈ 1.81 meters
the height of the tree is approximately 1.81 meters.