The measure of ∠A is 53.
The measure of ∠B is 37.
What is an expression?An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠A and ∠B are complementary.
This means,
∠A + ∠B = 90
Now,
∠A = 7x + 4
∠B = 4x + 9
7x + 4 + 4x + 9 = 90
11x + 13 = 90
11x = 90 - 13
11x = 77
x = 7
Now,
∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53
∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37
Thus,
∠A = 53
∠B = 37
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4 Write an expression
explaining the depth of
an Olympic pool that
goes to 50 ft. deep.
The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:
d = 50 ft.
What is olympic pool?
Olympic pool is a type of swimming pool that is used for competitive swimming and diving events. These pools typically have a uniform depth, a smooth and flat bottom and multiple lanes for swimmers to compete in.
The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:
d = 50 ft.
Where d is the depth of the pool. This expression simply states that the depth of the pool is equal to 50 ft.
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question 6
help me asap
The approximate length of arc CB is given as follows:
14.17 cm.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:
C = 6.28r.
The radius for this problem is given as follows:
r = 7 cm.
The angle relative to arc CB is given as follows:
2 x 58º = 116º.
As an entire circumference has an angle of 360º, the approximate length of arc CB is obtained as follows:
116/360 x 6.28 x 7 = 14.17 cm.
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Please help me by determining the value of the missing angle using the inverse trig function.
On solving the provided question, we cans ay that in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here, in this triangle by Pythagorean theorem
[tex]A^2 = B^2 + C^2[/tex]
AC = [tex]\sqrt{14^2 - 9^2}[/tex]
AC = [tex]\sqrt{196 - 81}[/tex]
AC = [tex]\sqrt{115}[/tex]
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You have a 6oz container and a 10oz container and a spout with unlimited water how do you measure exactly 8oz
Answer:
firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass
Step-by-step explanation:
The rate per cent per annum at which
$1200 is invested to gain $ 72 in simple
interest in three years is
(A) ½
(B) 2
(C)
(D)
9¹/2
18
A soccer player has a large cylindrical water cooler that measures 3.5 feet in diameter and is 2 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
The volume of the water in the water cooler when it is completely full is 82.21 gallons.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinitely curvilinear surface.
Given that the height of a cylinder is 3.5 feet. The diameter of the cylinder is 2 feet.
The radius of the cylinder is half of the diameter.
The radius of the cylinder is 2/2 = 1 foot.
The volume of a cylinder is πr²h.
r = radius, h = height
The volume of the cylinder is
π×1²×3.5
= 3.14 × 3.5
= 10.99 cubic foot
= 10.99 × 7.48 gallons
= 82.205 gallons
= 82.21 gallons
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The temperature at noon was $-4\degree$ C. By midnight, the temperature dropped $8\degree$ C. Which expression represents the temperature at midnight?
The temperature at midnight would be -4°C - 8°C since the temperature at noon was -4°C and at midnight it dropped 8°C.
The temperature at midnight would be -4°C minus 8°C, which can be expressed as:
-4°C - 8°C = -12°C
Therefore, the temperature at midnight would be -12°C.
Temperature is a measure of the degree of hotness or coldness of a body or an environment. It is a physical quantity that expresses the amount of thermal energy in a substance or a system, typically measured using a thermometer in units such as Celsius (°C) or Fahrenheit (°F). In general, the higher the temperature, the more thermal energy is present in the system, and the lower the temperature, the less thermal energy is present.
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The following table shows the length (in days) of each of the
9
99 Tucker family vacations.
Based on this data, what is a reasonable estimate of the probability that the next Tucker family vacation lasts less than
3
33 days?
Answer:because
Step-by-step explanation:a
Answer: 0.56
Step-by-step explanation:
She has to be at the airport at least 100 minutes before the flight. By what time must she arrive at the airport?
She has to be at the airport at least 100 minutes before the flight. She must arrive at the airport at least two hours and 120 minutes before the flight.
Which ensures that she has time to check in, go through security and passport control, and board the flight. the amount f time a passenger needs to arrive before the flight can vary depending on the airline and airport. Generally, most airlines recommend that passengers arrive at the airport at least two hours before domestic flights and three hours before international flights.
In order it gives the passenger enough time to get to the airport depending on the location and traffic, check in and drop off any luggage, go through security and passport control, then at last board the flight
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One year, the population of a city was 322,000. Several years later it was 273,700. Find the percent decrease.
The population of the city has decreased by 15%.
Percentage refers to a way of expressing a number as a fraction of 100, and is often represented by the symbol (%).
To find the percent decrease, we need to determine the difference between the original population and the new population. We can do this by subtracting the new population from the original population:
322,000 - 273,700 = 48,300
This means that the population has decreased by 48,300. To find the percentage decrease, we need to express this as a percentage of the original population. We can do this by dividing the decrease by the original population and then multiplying by 100:
(48,300 / 322,000) x 100 = 15%
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Please help me on this I am confused find the value of x pls pls pls pls pls pls pls pls pls pls pls pls pls.
The value of x is given as follows:
x = 130º.
How to obtain the value of x?To obtain the value of x, we must consider the exterior angle theorem, which states that each interior angle is supplementary with it's interior angle, meaning that the sum of their measures is of 180º.
As the interior angle is of 50º, the measure of the exterior angle x is given as follows:
x = 180 - 50
x = 130º.
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the mariana trench is about 11km deep. mount everest is about 29,000 ft high. what is the total height change from the top of mount everest to the bottom of the mariana trench, expressed in miles?
Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles
We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles
Depth of Mariana Trench (d) = 11 km = 11 × 0.62136
= 6.835 miles
Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189
= 5.492 miles
Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by
H = Depth of Mariana Trench + Height of Mount Everest
H = d + h
H = 6.835 miles + 5.492 miles
H = 12.327 miles
H = 12.3 miles
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Indicate whether each value will make the inequality 15<3x true. Drag True or False to the appropriate values: 5.6,5,3,6,7 3/4,4.5.
Answer:
So, for the values 5.6, 6, and 7, the inequality 15 < 3x is true. For the values 5, 3, 3/4, and 4.5, the inequality 15 < 3x is false.
Step-by-step explanation:
For the inequality 15 < 3x to be true, 3x must be greater than 15. To determine whether each value will make the inequality true, we can substitute each value for x and see if the inequality holds.
For x = 5.6, 3x = 16.8, which is greater than 15, so the inequality is true and the value 5.6 makes the inequality true.
For x = 5, 3x = 15, which is equal to 15, so the inequality is false and the value 5 does not make the inequality true.
For x = 3, 3x = 9, which is less than 15, so the inequality is false and the value 3 does not make the inequality true.
For x = 6, 3x = 18, which is greater than 15, so the inequality is true and the value 6 makes the inequality true.
For x = 7, 3x = 21, which is greater than 15, so the inequality is true and the value 7 makes the inequality true.
For x = 3/4, 3x = 2.25, which is less than 15, so the inequality is false and the value 3/4 does not make the inequality true.
For x = 4.5, 3x = 13.5, which is less than 15, so the inequality is false and the value 4.5 does not make the inequality true.
So, for the values 5.6, 6, and 7, the inequality 15 < 3x is true. For the values 5, 3, 3/4, and 4.5, the inequality 15 < 3x is false.
The figure on the right is a scaled copy of the figure on the left. Which side in the figure on the right corresponds to segment DF? What is the scale factor?
The side which corresponds to QS is VU, and the scale factor is 2.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Given that, the figure on the right is a scaled copy of the figure on the left.
We need to find the corresponding side of QS and scale factor,
The figure is 90° counterclockwise rotated,
Therefore,
The corresponding sides are:
PR ~ TW
RQ ~ VT
QS ~ UV
PS ~ WU
∵ the measure of QS = 4 units and the measure of UV = 2 units
∴ scale factor = 4/2 = 2
Hence, the side which corresponds to QS is VU, and the scale factor is 2.
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The question do not contain figure, the similar question is solved.
two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart. Find the speed of the trains.
The speed of both the trains would be 400 mph and 450 mph respectively.
What is the formula to calculate the distance travelled?The formula to calculate the distance travelled is -
Distance = Speed x Time
Given is that two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart.
Let the speed of one train be {x} mph. Then, the speed of the other train would be {x + 10} mph.
Distance covered by both the trains would be -
train { 1 } = 5x ... { 1 }
train { 2 } = 5(x + 10) ... { 2 }
Now, we can write -
1020 - {5x + 5(x + 10)} = 170
1020 - 170 = 10x + 50
10x = 800
x = 80
Speed of train { 1 } = 400 mph
Speed of train { 2 } = 450 mph
Therefore, the speed of both the trains would be 400 mph and 450 mph respectively.
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the mayor of a town believes that above 72% of the residents favor annexation of an adjoining community. is there sufficient evidence at the 0.05 level to support the mayor's claim? state the null and alternative hypotheses for the above scenario.
Null hypothesis: Proportion of residents favoring annexation <= 72%. Alternative hypothesis: Proportion of residents favoring annexation > 72%
The null hypothesis is that the proportion of residents who favor annexation is equal to or less than 72%. The alternative hypothesis is that the proportion of residents who favor annexation is greater than 72%.
To determine if there is sufficient evidence to support the mayor's claim, a hypothesis test should be performed. A common approach is to use a one-sample proportion test. This test compares the proportion of residents who favor annexation in a sample to the hypothesized proportion of 0.72.
Assuming a significance level of 0.05, if the p-value is less than 0.05, then there is sufficient evidence to reject the null hypothesis and conclude that the proportion of residents who favor annexation is greater than 72%.
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34 on april 18, 1775, paul revere set off on his midnight ride from charlestown to lexington. if he had ridden straight to lexington without stopping, he would have traveled 11 miles in 26 minutes. in such a ride, what would the average speed of his horse have b
The average speed of Paul Revere's horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.
To find the average speed of Paul Revere's horse, we can use the formula:
average speed = total distance / total time
In this case, the total distance is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).
So, the average speed of Paul Revere's horse would be:
average speed = 11 miles / 0.4333 hours
average speed ≈ 25.4 miles per hour
Therefore, the average speed of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.
Using the formula for average speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.
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The complete question is:
On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?
Help ASAP.............
Answer: about 1587 cm^2
Step-by-step explanation: The equation for area of circle is A= πr^2 OR A= (pi/4)d^2
Given the diameter is 46.7, the radius would be half of that which is 23.35.
Simply plug it into the equation
A = π23.35^2
OR
A= (π/4)46.7^2
Since you are using 3 in place of pie, it would be 3(23.35)^2 OR (3/4)46.7^2
the answer i got was 1,635 cm^2 so your closest choice to that is 4
christian has a collection of 18 shark teeth. he identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as bull shark teeth, what does the ration 6:8 represent in this situation
Answer:
Check below
Step-by-step explanation:
Number of tiger shark teeth = 6
Number of sand shark teeth = 8
Number of tiger shark teeth : Number of sand shark teeth
6 : 8
∴ 6 : 8 ratio representation
Answer:
6:8
Step-by-step explanation:
need help with this asap please!!
Answer:
A van can carry 18 students; a bus can carry 41 students.
Step-by-step explanation:
Let v = capacity of van.
Let b = capacity of bus.
School A:
3v + 12b = 546
School B:
13v + 6b = 480
Our system of equation is:
3v + 12b = 546
13v + 6b = 480
3v + 12b = 546
+ -26v - 12b = -960
-----------------------------
-23v = -414
v = 18
3v + 12b = 546
3(18) + 12b = 546
54 + 12b = 546
12b = 492
b = 41
Answer: A van can carry 18 students; a bus can carry 41 students.
Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval
A. True
B. False
Option A. TRUE. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.
The Intermediate Value Theorem is a fundamental theorem in mathematics that states that, for any given continuous function on an interval, every value between the minimum and maximum values of the function on the interval must be taken by the function at some point within the interval. This theorem states that, given a function f defined on an interval [a, b], if f(a) and f(b) have different signs (i.e. one is positive and the other is negative), then there exists at least one c in the interval (a, b) such that f(c) = 0. The theorem is important because it guarantees the existence of solutions to certain types of equations, and it is widely used in calculus, engineering, physics, and many other fields.
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Jayden and Ramon are members of a bowling league. Jayden plans to order
custom team shirts and he has narrowed his options down to two companies.
Designs n More will charge a $10 design fee and $7.50.per shirt: Custom
Creations charges $9 per shirt and does not charge a design fee.
Equating the mathematical expressions, for the total costs of both companies to be the same, Jayden and Ramon must buy about 7 shirts.
What is a mathematical expression?A mathematical expression consists of the combination of variables, values, constants, and numbers using mathematical operands.
A mathematical expression is not the same as an equation, which states that two mathematical expressions are equal.
Designs n More Custom Creations
Design Fee $10 $0
Variable cost per shirt $7.50 $9.00
Let the number of shirts = x
Designs n More's total costs = 10 + 7.5x ... Expression 1
Custom Creations' total costs = 9x ... Expression 2
For the total costs of both companies to be the same, the two expressions for their total costs will be equal:
10 + 7.5x = 9x
10 = 1.5x
x ≈ 7
Thus, approximately, 7 shirts need to be bought for the total costs to be the same.
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Question Completion:How many shirts will make the two companies' total costs the same?
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
The mean would be 35 feet.
The mean tells us that the typical throw of the ball results in a distance of approximately 3.5 feet.
what is Mean?
In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.
To find the mean of the distances, we need to calculate the sum of all the distances and divide by the total number of distances:
(20+25+25+31+33+34+41+41+45+50+56+67) / 12 = 425 / 12 = 35.42
Rounding to one decimal place, we get the mean distance of approximately 3.5 feet.
However, it's worth noting that the stem-and-leaf plot shows some variability in the distances, with some throws going as far as 6.7 feet and some as short as 2 feet.
So while the mean can provide us with a measure of central tendency, it doesn't tell the whole story about the distribution of the distances.
Therefore, The mean would be 35 feet. The mean tells us that the typical throw of the ball results in a distance of approximately 3.5 feet.
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A plant is already 9 centimeters tall, and it will grow one centimeter every month.
Let be the plant's height (in centimeters) after months.
Write an equation relating to . Then graph your equation using the axes below.
Answer:
p + (m × 1) = t
If a plant is already ___cm tall and it will grow one cm every month, an equation to find out how much the plant grew in __ months is this:
(Let t = total number of centimeters, m = number of months, and p = the length of the plant already.)
p + (m × 1) = tTherefore, the equation you can use is p + (m × 1) = t.
Look at the image below.
Answer: 28 (look at the image for the solution)
Step-by-step explanation:
Answer:
A = base x height
A = 7 x 4
A = 28
Have a wonderful day! :-)
12.5 × 1.989 pls help me
You take an SRS of size 500 from the 37,000 students at Purdue University and measure individual’s heights. You then take an SRS of size 250 from the 4,400,000 adults in the state of Indiana and measure their heights. Assuming the standard deviation of individual heights in the two populations is the same, the standard
deviation of the sampling distribution of mean heights for the Indiana sample is
(a) larger than for the Purdue sample because the sample size is smaller.
(b) larger than for the Purdue sample because it uses a smaller fraction of the population.
(c) smaller than for the Purdue sample because the sample size is smaller.
(d) smaller than for the Purdue sample because it uses a smaller fraction of the population.
(e) impossible to determine because of sampling variability.
Larger than for the Purdue sample because the sample size is smaller. Therefore, the option A is the correct answer.
What is margin of error?Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
Given sample size = 500
Total outcomes = 37,000
The margin of error in a 95% confidence
The margin of error is given by
Margin of error (statistic) = Critical value x Standard error of the sample.
So, according to the given condition margin of error in a 95% confidence is same as for the Purdue sample because both are samples of size 500, because it depends on sample size.
Therefore, the option A is the correct answer.
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jack bought a bike that was 35% off the original price let p represent the original price. what expressions can be used to calulate the sale price
The expression used to calculate the sale price is given as follows:
S(p) = 0.65p.
How to obtain the sale price?The expression used to calculate the sale price is obtained applying the proportions in the context of the problem.
The price was 35% off, meaning that there was a discount of 35%, meaning that a percentage of 100 - 35 = 65% of the total price was paid, hence the expression used to calculate the sale price is given as follows:
S(p) = 0.65p.
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I NEED HELP, THIS IS DUE TODAY AND IM CONFUSED.
The value of x that makes the shape a parallelogram is 2/3
What is a quadrilateral?A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.
A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.
From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:
6x = 3x + 2
3x = 2
x = 2/3
The value of x is 2/3
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A dust particle weighs around 7.53 x 10-16 grams.
grams
O 7,530,000,000,000,000,000
0.0000000000000753 grams
75, 300,000,000,000,000 grams
O 0.0000000000000000753 grams
O'0.0
0.000000000000000753 grams
Answer:
It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.
Step-by-step explanation:
