Answer:
atq= let no.be x and y
x= 4y-3.......(1)
x-2y=7....(2)
subtracting both eqn
x-x+2y=4y-3-7
2y=4y-10
-2y= -10
y=5 ........second no.
first no...x=7+2y=7+10=17.......first no.
Step-by-step explanation:
A ladder 50m long is placed on the ground in such a way that it touches the top of vertical wall 30m high. Find the distance of the foot of the ladder from the bottom of the wall
The distance between the foot of the ladder from the bottom of the wall is 40 meters.
What is the Pythagorean theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Here,
The distance between the foot of the ladder from the bottom of the wall can be found by using the Pythagorean theorem.
The ladder is the hypotenuse, with a length of 50m
The distance from the wall to the ground is 30m
The distance from the wall to the foot of the ladder is x
Using the Pythagorean theorem:
x² + 30² = 50²
x² + 900 = 2500
x² = 1600
x = 40
So, the distance between the foot of the ladder from the bottom of the wall is 40 meters.
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Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05.What does Bob conclude?
A correlation coefficient of 0.05 indicates a very weak positive correlation between the number of bedrooms and selling price.
When Bob calculates the correlation between the number of bedrooms in a home and its selling price and obtains a value of only 0.05, he can conclude that there is little to no linear relationship between the two variables.
Correlation is a statistical measure that indicates the degree to which two variables are related and the direction of the relationship. A correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
A correlation coefficient of 0.05 is very close to 0, indicating that there is almost no linear relationship between the number of bedrooms in a home and its selling price.
However, it is important to note that a low correlation coefficient does not necessarily mean that there is no relationship between the variables, as there could be a non-linear relationship or other types of relationships that cannot be captured by a correlation coefficient.
Therefore, Bob should further analyze the data set and explore other statistical measures or techniques to fully understand the relationship between the number of bedrooms in a home and its selling price.
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Bill is ordering 30 basketball jerseys. Two companies gave their bid: “print it”charges $21.50 per shirt. “ top print” charges a flat fee of $70.00, then $18.00 for each shirt
which company should bill use?
Bill should use the "Print It"company.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
To determine which company Bill should use, you need to calculate the total cost of each option and compare them.
For "Print It," the total cost would be :
= 30 x $21.50
Apply the multiplication operation, and we get
= $645.00
For "Top Print," the total cost would be :
= $70.00 + (30 x $18.00)
= $690.00
Since the cost of "Print It" is lower than "Top Print," Bill should use "Print It" as it would be a more cost-effective option for him.
Thus, he should use the "Print It"company.
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of the following is the correct label to show volume?
O inches
O ft²
O m³
O square centimeters
Answer:
О m³ (cubic meters)
Step-by-step explanation:
The volume formula is length * width * height
Example:
volume = 3m * 5m * 4m
volume = 60m³
The solution is, О m³ (cubic meters), is the correct label to show volume.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
to find the correct label to show volume.
now, we know that,
The volume formula is length * width * height
as we know that,
the standard unit for length is meter (m).
now, we have,
length has unit m
width (= length) has unit m
and, height (=length) has unit m
so, we get,
Volume = length * width * height
= m * m* m (as unit)
= m³
Example:
volume = 3m * 5m * 4m
volume = 60m³
Hence, The solution is, О m³ (cubic meters), is the correct label to show volume.
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if the product is -8 and the sum is 2 what are the other 2 numbers?
Answer:
4 and -2
Step-by-step explanation:
4 + -2 = 2
4 x -2 = -8
) This afternoon Beth left school, rode the bus 1/2 of a mile, and then walked 1/12 of a mile to get home. How much farther did Beth ride than walk?
Using this formula, we find that d = 2/3, meaning Beth rode 2/3 of a mile farther than she walked. The formula to solve this problem is d = 1/2 - 1/12, where d is the difference in distance between the bus ride and the walk.
Beth rode the bus 1/2 of a mile and then walked 1/12 of a mile to get home. To calculate how much farther she rode than walked, we need to subtract the distance walked from the distance ridden. The formula to solve this problem is d = 1/2 - 1/12, where d is the difference in distance between the bus ride and the walk. Using this formula, we find that d = 2/3, meaning Beth rode 2/3 of a mile farther than she walked.
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Can someone help me with this question ??
The length of x is given as follows:
x = 3.6.
What are similar polygons?Similar polygons share these two features listed as follows:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.In the context of this problem, the proportional relationship for the side lengths of the polygons is given as follows:
x/3 = 2.4/2 = 4.8/4 = 6/5.
The relationship can be simplified as follows:
x/3 = 1.2.
Applying cross multiplication, the value of x is obtained as follows:
x = 3 x 1.2
x = 3.6.
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Denton
When mapped on a coordinate plane, the coordinates of 2 of the towns are Albion (5, 5) and Denton (-7,-3). Beacon
is exactly in the middle of Albion and Denton, and Casper is exactly in the middle of Denton and Beacon.
What are the coordinates of Casper?
The coordinates of Casper which lies exactly in the middle of Denton and Beacon are (-4, -1).
What are the Coordinates?Coordinates are defined as the set of points in a coordinate plane or space, which describes the position of that point in that plane or space.
In a coordinate plane, the midpoint of two points (x₁, y₁) and (x₂, y₂) is the point (x, y) such that their measures are,
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
First, we can write the given measures.
Coordinates of Albion = (5, 5)
Coordinates of Denton = (-7, -3)
Given that, Beacon is lying exactly in the middle of Albion and Denton.
Let the coordinates of Beacon be (x, y).
Using the formula above,
x coordinate of Beacon = (5 + -7) / 2 = -1
y coordinate of Beacon = (5 + -3) / 2 = 1
Coordinates of Beacon are thus (-1, 1).
Casper is lying exactly in the middle of Denton(-7, -3) and Beacon (-1, 1).
Let (x' , y') be the coordinates of Casper.
Using the same formula,
x' = (-7 + -1) / 2 = -4
y' = (-3 + 1) / 2 = -1
Hence the coordinates of Casper are (-4, -1).
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how many vertices and edges dose this shape have?
Vertices :
Edges:
Step-by-step explanation: A vertex is a corner on shape. And edge is a line segment between faces. A face is singular flat surface.
In 10 words or fewer, write your own definition of slope.
Answer: An incline, a slant up or down.
Step-by-step explanation:
Mai spent $9 on fruit at the grocery store. She spent a total of $15 at the store. What percentage of the total did she spend on fruit?
Answer:
Mai spent 60% of her total spending on fruit
Step-by-step explanation:
To find the percentage of the total spent on fruit, we can divide the amount spent on fruit by the total amount paid and multiply by 100 to express the answer as a percentage.
First, let's find the amount spent on things other than fruit: $15 total spent - $9 spent on fruit = $6 spent on other things.
Next, we divide the amount spent on fruit by the total amount spent: $9 on fruit / $15 total spent = 0.6.
Finally, we multiply by 100 to express the answer as a percentage: 0.6 * 100 = 60%.
So Mai spent 60% of her total spending on fruit.
A boat heading out to sea starts out at Point A, at a horizontal distance of 724 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 16 ∘ . At some later time, the crew measures the angle of elevation from point B to be 5 ∘ . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is 1496 ft.
What is distance?Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
Given that, a boat is at point A which at 724 ft distance from a lighthouse making an angle of elevation to the lighthouse’s beacon-light of 16°, when moved to some distance B making an angle of elevation to the lighthouse’s beacon-light of 5°, we need to find the distance from point A to point B.
Refer to the figure attached,
The whole scene is creating two right triangles, rt Δ CDA and rt Δ CDB
Using the trigonometric functions, in rt Δ CDA,
We have,
tan 16° = CD/DA
CD = tan 16° × 724
CD = 207.6
Therefore, the height of the lighthouse is 207.6 ft
Now,
tan 5° = CD/DB
DB = CD / tan 5°
DB = 2373
The distance between A and B = DB-DA = 2373 - 724 = 1496
Hence, the distance from point A to point B is 1496 ft.
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Please help me by finding the missing side length using trig!
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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pls im not understanding anything and its a test
Determine whether each statement is true or false. Choose "True" or "False" for each statement.
Response area with 6 radio buttons within 3 groups.
Statement True or False?
An elevation of negative 25 feet is less than an elevation of 0 feet.
True
False
An elevation of negative 25 feet is greater than an elevation of 5 feet.
True
False
An elevation of negative 25 feet is less than an elevation of negative 5 feet.
True
False
An elevation of negative 25 feet is less than an elevation of 0 feet: True.
An elevation of negative 25 feet is greater than an elevation of 5 feet: False.
An elevation of negative 25 feet is less than an elevation of negative 5 feet: True.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In this context, we can reasonably infer and logically deduce that all numerical values (numbers) to the left are always less than numerical values (numbers) located to the right of a number line such as the following:
-25 < 0.
-25 < 5.
-25 < -5.
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c. 3x - y = 7
y = 3x - 2
Answer:
Step-by-step explanation:
3x- (3x-2)=7
- (3x-2) = -3x+2
3x-3x=0x
so the answer is zero or imposible becasue nothing can be times by zero
Gloria traveled a total of 888 miles to get from school to her apartment. Gloria took the bus from school and then walked the remaining 880880880 yards home.
Gloria walked 500500 Miles from nearest bus stop to home.
How to convert yards into miles ?
To convert a yard measurement to a mile measurement, divide the length by the conversion ratio.
Since one mile is equal to 1,760 yards, you can use this simple formula to convert:
miles = yards ÷ 1,760
The length in miles is equal to the yards divided by 1,760.
Given:
Gloria traveled : 888 miles
1 Mile = 1760 yards
880880880 yards = 500500 Miles
So she walked 500500 Miles from nearest bus stop to home.
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f(x)=x^2-4x+3 find the quadratic function
Answer:
Step-by-step explanation:
Which collection of three side lengths WILL NOT form a triangle?
10 in, 12 in, 15 in
10 in, 15 in, 6 in
4 in, 5 in, 10in
9in, 16 in, 8 in
The collection of 4 in, 5 in, and 10in of three side lengths will not form a triangle.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.
Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, A triangle has a property that the sum of any two sides is always greater than the third side and the difference between any two sides is smaller than the third side.
From the given options if we observe the third option,
4 + 5 should be greater than 10 but it is not therefore, It is the correct option.
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how many uniforms can you make
Answer:
39
Step-by-step explanation:
165 and 3/4 is equal to 165.75 and 4 and 1/4 is 4.25
165.75/4.25=39
39 uniforms could be made
8 in x 3 in x 2 in. of 8 inches x 10 inches
Answer: imma say do 8x3x2= the answer you get then 8x10= the answer you get then multiply the two answer you get that should be you answer.
Step-by-step explanation: hope this helps
What is the slope of the line that contains these points?
xxx 888 111111 141414 171717
yyy 363636 121212 -12−12minus, 12 -36−36minus, 36
The slope of the given straight line passing through the coordinates given would be -8.
What is the general equation of a straight line?The general equation of a straight line is → Ax + By + C = 0Rearranging the equation, we can write -By + C = - Ax
By = - Ax - C
y = -(A/B)x - (C/B)
Given are the coordinate points lying on the line.
Slope of a line measures the rate of change of {y} with respect to {x}.Mathematically, we can write the slope as → m = (y₂ - y₁)/(x₂ - x₁)We can write the slope as -
m = (y₂ - y₁)/(x₂ - x₁)
m = {12 - 36}/{11 - 8}
m = -24/3
m = -8
Therefore, the slope of the given straight line passing through the coordinates given would be -8.
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Classify the triangle by its sides.
A.acute
B.scalene
C.isosceles
D.equilatera
Answer:
D because all sides are equal
Question 10:
A plumber cut a
pipe into 5
equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
If a plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. the length of the first pipe originally is 702 cm.
How to find the length?Let's call the original length of the first pipe "L"
Let the length of each of the 5 equal pieces "x".
set up the equation:
5x + 27 = L
Each piece of the second pipe is "x" cm long. The second pipe is 15 m long, which is equivalent to 1500 cm. The plumber cut 11 pieces of the same length as each of the 5 equal pieces from the first pipe, so the total length of the 11 pieces is:
11x
The plumber had 15 cm of the second pipe left over after cutting 11 pieces, so we can set up another equation:
1500 - 11x = 15
Solving for "x" in the second equation:
11x = 1485
x = 135
So each piece of the second pipe is 135 cm long.
To find the original length of the first pipe, we can substitute x = 135 into the first equation and solve for L:
5x + 27 = L
5(135) + 27 = L
L = 702
Therefore, the original length of the first pipe was 702 cm.
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what is the solution to the number sentence 18= b/-3 -4
Answer:
b = -66.
Step-by-step explanation:
[tex]18 = \frac{b}{ - 3} - 4 \\ = - 3(18) = - 3 \times \frac{b}{ - 3} - 4( - 3) \\ = - 54 = b + 12 \\ = - 54 - 12 = b \\ = - 66 = b[/tex]
A large milling machine shaves 2-in. from a plate that is 1 in. thick. What is the thickness of the plate after one pass? What is the thickness of the plate after three passes?
The thickness of the plate after one pass is 1 21/ 32 and after three pass is 1 7/32 in.
How to convert mixed fractions?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
An inappropriate fraction is created by adding the numerator to a mixed fraction after multiplying the denominator of the proper fraction by the whole number it is related to.
How change a fraction into a mixed fraction?
By denominator, divide the numerator.
Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.
Given that the thickness of the plate is 1 7/8 in.
Convert the mixed fraction into improper fraction:
1 7/8 = 15/8
The machine shaves of 7/32 in, thus after one pass we have:
15/8 - 7/32
Take the LCM:
60/32 - 7/32 = 53/32
Covert the fraction into mixed fraction:
53/32 = 1 21/ 32 in
After three passes through the machine the thickness of the plate is:
15/8 - 3(7/32)
60/32 - 21/32 = 39/32
Covert into mixed fraction:
39/32 = 1 7/32 in
Hence, the thickness of the plate after one pass is 1 21/ 32 and after three pass is 1 7/32 in.
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The correct question is:
the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.T/F
The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.
False.
It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.
It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.
In other words, the probability of the intersection and the probability of the union are subsets of one another.
The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.
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How to solve this with sin, cos, or tangent
The area of the triangle is 72 units².
How to find the area of a triangle?The area of a triangle can be found using sine as follows:
area of a triangle = 1 / 2 ab sin C
Hence,
a = 12 b = 24C = 30 degreesTherefore,
area of a triangle = 1 / 2 × 12 × 24 × sin 30
area of a triangle = 1 / 2 × 288 × sin 30
area of a triangle = 1 / 2 × 288 × 0.5
area of a triangle = 1 / 2 × 144
area of a triangle = 72 units²
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Surface area of a cube is 150m².The length of its edge is
Answer:
the length of the edge of the cube is 5 meters
Step-by-step explanation:
The surface area of a cube can be found using the formula:
Surface Area = 6 x (side length)^2.
Since the surface area of this cube is 150 square meters, we can set up an equation to solve for the side length:
150 = 6 x (side length)^2
Dividing both sides by 6, we get:
25 = (side length)^2
Taking the square root of both sides, we find the side length:
side length = sqrt(25) = 5 meters.
So the length of the edge of the cube is 5 meters.
Answer:
Step-by-step explanation:
60(12*5) as a square has 4 on the top same for the bottom and has 4 vertices. I hope this helps
a company has 4 service trucks. let x represent the number of trucks that are not working at any point in time. consider the probability model shown below for x. x 0 1 2 3 4 probability 0.2 0.24 0.17 0.06 0.33 a. what is the probability that exactly 1 of the trucks are not working at any point in time? give your answer to two decimal places. 0.24 b. what is the probability that fewer than 1 of the trucks are not working at any point in time? give your answer to two decimal places. 0.26 c. what is the probability that more than 1 of the trucks are not working at any point in time? give your answer to two decimal places.
Probability of each of the following is,
(a) 0.24, (b) 0.20 and (c) 0.56
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
(a) From the table,
Probability that exactly 1 of the trucks are not working at any point in time = P(x = 1) = 0.24.
(b) Probability that fewer than 1 of the trucks are not working at any point in time is the probability that no trucks are working at any point of time.
P(x < 1) = P(x = 0) = 0.20
(c) Probability that more than 1 of the trucks are not working at any point in time is the combined probability that 2, 3 and 4 trucks are working.
P(x > 1) = P(x = 2) + P(x = 3) + P(x = 4)
= 0.17 + 0.06 + 0.33
= 0.56
Hence each of the values of the probability is found.
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