what is the area?
write your answer as a fraction or as a whole or mixed number
\( \underline \mathcal \pink{ GIVEN}\)
Base = 2 9/10 kmHeight = 4 6/7 km\( \underline \mathcal \purple{ TO \: FIND}\)
Area of the triangle\( \underline \mathcal \blue{CALCULATION}\)
\( \qquad \tt \leadsto \: area = \frac{1}{2} \times base \times height\)
\( \qquad \bf \nrightarrow \: area = \frac{1}{ \cancel2} \times \cancel2 \frac{9}{10} \times 4 \frac{6}{7} \)
\( \qquad \bf \nrightarrow \: area = \frac{9}{ \cancel{10}} \times \cancel4 \frac{6}{7} \)
\( \qquad \bf \nrightarrow \: area = \frac{9}{ 5} \times 2 \frac{6}{7} \)
\( \qquad \bf \nrightarrow \: area = \frac{108}{ 35} \approx3.08 \: {km}^{2} \)
Thus, The area of the triangle is 3.08 kilometers...~
GAMES Darius is playing a bowling game where he rolls balls into a 10-point hole or a 25-point hole. He rolls a total of 11 balls, and his score is 215 points. Write a system of equations to represent the information and use substitution to determine how many balls Darius rolled into each hole.
By solving the system of equations, we found that the number of balls rolled in 10 point hole is 4 and the number of balls rolled in 25 point hole is 7.
What is meant by the system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions of systems of equations.
Given,
Total number of balls rolled = 11
Total points scored = 215
Let the number of 10-point balls rolled by Darius be x and the number of 25-point balls rolled be y.
We can now write a system of equations, using the given information.
x + y = 11
10x + 25y = 215
On solving this system of equations, we can find the values of x and y.
Multiply the first equation by 10.
10x + 10y = 110
10x + 25y = 215
Now subtract the equations.
-15y = -105
y = 7
Now find x by substituting y in any equation.
x + y = 11
x + 7 = 11
x = 4
Therefore by solving the system of equations, we found that the number of balls rolled in 10 point hole is 4 and the number of balls rolled in 25 point hole is 7.
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if paul and Steve are the same height and they are both correct write and equationto represent this relationship put puals expresiion on the left side of the equal sign and steves expression on the right
Answer:
Paul=Steve
Step-by-step explanation:
Answer:
The expression that represents Paul’s height in inches is 3/4t - 16. The expression that represents Steve’s height in inches is 4/3t - 6. Paul and Steve are the same height, so the equation that represents this relationship is
3/2t - 16 = 4/3t - 6
( PLATO/EDMENTUM ANSWER)
determine the solutions of the equation: absolute value of the quantity one fifth times x plus 2 end quantity minus 6 equals two.
Answer: The solutions of the absolute value equation are given by:
x = -41 and x = 49.
What is the absolute value function?
The absolute value function is defined by:
|x| = x, x >= 0.
|x| = -x, x < 0.
The absolute value function measures the distance of a point x to the origin, that is, the distance to x = 0. From this, we get that |x| = a can mean either that:
x = a, or;
x = -a.
In this problem, the equation is given by:
Hence:
0.2|x - 4| = 9
|x - 4| = 45
The first possible solution is:
x - 4 = 45
x = 49.
The second possible solution is:
-x + 4 = 45
-x = 41
x = -41.
Hence the solutions are x = -41 and x = 49.
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Step-by-step explanation:
50 points and BRAINLIEST
Answer:
AZ = 12.80
Step-by-step explanation:
There are 2 triangles in the square XARS. Squares are always congruent, all sides are the same. Given that WT is 6, we can assume that RS is also 6 (because of congruency). RA is is the hypotenuse of the triangle ARS. To find AS, we can plug in the pythagorean theorem 6^2+x=^2=10^2. We end up getting square root of 64 which simplifies to 8. AS is now 8. We also know that ST is 6 since the square WRST has all congruent sides. 8+6=14 gives us line AT. TZ is 8 due to triangle XAR and the congruency theorem. Now we plug in pythagorean theorem to find AZ and we get 8^2+10^2=x^2. After simplifying the square root of 164, we see that AZ is equal to 12.80
Answer:
12.80
Step-by-step explanation:
SO IT IS 12.80 BECAUSE IT IS 12.80. SIMLIFY TO 12.8 SO YEAH!!
HOPE YOU UNDERSTAND.
Answer the following questions.
1. Trish can complete 10 problems in 60 minutes. At this rate, could she complete 25 problems in 130 minutes? Write your answer as YES or
NO.
Convert -145 degrees to radians.
Answer:
\(\frac{-29}{36}\)π
Step-by-step explanation:
Which of the values is the best estimate of the correlation coefficient for the line of best fit shown in the scatter plot?
0.9
0.4
-0.4
0.9
The correlation coefficient that would best describe the line of best fit shown in the scatter plot is 0.9 which is a weak positive correlation.
What is correlation?The statistical concept of correlation describes how closely two variables move in tandem with one another.
We can see that Slope is not near to horizontal, thus Correlation Coefficient will be greater than 0.5
Since the value of X axis is get increased, then the value of Y axis is also increasing.
According to the graph is scattered in such a way that, if we draw a line from the centre, we can observe that as 'x' increases 'y' also increases, then the relation is positive correlation.
Therefore, the given scatter plot shows positive weak correlation with value 0.9 .
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list 5 other statistical measures that we could use to measure our ""well being"" other than gdp?
Human Development Index (HDI), Gross National Happiness (GNH), Happy Planet Index (HPI), Better Life Index (BLI), and Genuine Progress Indicator (GPI) are statistical measures that we could use to measure our "well-being" other than GDP.
These measures are important because GDP alone does not provide a complete picture of a country's well-being. GDP measures the market value of goods and services produced within a country, but it does not take into account factors such as income distribution, environmental quality, and social well-being.
By using these additional measures, we can gain a more comprehensive understanding of a country's progress and its impact on people and the planet.
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9. You visit an aquarium. On of the
tanks hold 450 gallons of water. Draw
a diagram to show one possible set of
dimensions of the tank.
The aquarium would have a volume of 103950 cubic inches. Its dimensions are shown in the image attached.
What is an aquarium?An aquarium is a container, often made of glass or acrylic, in which aquatic plants and animals are kept for display or research purposes. It can also be a building or room that houses such tanks.
We have been told that the volume of the water that can be held by the aquarium is 450 gallons of water. If we convert the gallons to cubic inches we would obtain 103950 cubic inches. The dimensions of the aquarium must therefore be such that it would a volume of 103950 cubic inches.
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what is rad to degree?
Radians are multiplied by 180° radians to convert to degrees.
A unit of measurement for angles that is about 57.3°, or the angle covered in the center of a circle by an arc that has the same length as the radius.
Conversion factor between radians and degrees
One radian, or degree, equals 0.01745329252:
1° = π/180°
0.005555556π = 0.01745329252 rad
There are 57.295779513 radians in a degree.
1 rad = 180°/π \s= 57.295779513°
The angle in degrees is equal to the angle in radians times 180 degrees divided by the constant pi: degrees = radians 180° /
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When solving the equation 6x - 8 = 12, the first step is to move the
constant, 8, to the right side by adding 8 to both sides. What is the
equation after step one?*
6x - 8 = 12 + 8
14x - 8 = 20
6x = 12 + 8
6x = 20
Answer:
6x= 12+8
Step-by-step explanation:
Which point represents the unit rate?
Graph the equation: y=4x+2
Answer:
Step-by-step explanation:
I used the site desmos
draw this graph I attached on graph paper
The estimate on an explanatory variable is not statistically significant at the 5%-level if the t-statistic is greater than 2.5. the p-value is less than 0.05. the 95% confidence interval does not contain zero. the 95% confidence interval contains zero.
The estimated value of the explanatory variable is not statistically significant at the 5%-level if a. the t-statistic is greater than 2.5.
The t-test is a hypothesis testing technique used to decide whether the estimated coefficient of a linear regression model is statistically significant or not. The t-value is used to measure the size of the difference between the estimated coefficient and the hypothesized value. When the t-value exceeds a critical value, such as 2.5, the estimated value of the explanatory variable is not significant at the 5%-level. It implies that the null hypothesis, which assumes that the explanatory variable's coefficient is zero, cannot be rejected.
The p-value is a measure of the probability of obtaining a more extreme value of the test statistic than the observed value if the null hypothesis is true. A small p-value implies that the null hypothesis should be rejected. When the p-value is less than 0.05, it means that the estimated value of the explanatory variable is significant at the 5%-level.
The confidence interval is a range of values that is expected to include the true value of the population parameter with a specified level of confidence. A 95% confidence interval means that the true value of the population parameter lies within the range 95% of the time. The 95% confidence interval does not contain zero implies that the estimated value of the explanatory variable is statistically significant at the 5%-level since it suggests that the population parameter is different from zero at the 5%-level. Conversely, if the 95% confidence interval contains zero, the estimated value of the explanatory variable is not statistically significant at the 5%-level since it means that the population parameter is not different from zero at the 5%-level. Therefore, it is essential to examine the t-statistic, p-value, and confidence interval while conducting hypothesis testing to make an informed decision.
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Question 1
1 pts
If the shortest side of a right triangle is 8, what are the two other sides that form a triple.
Answer:
8, 15, 17
Step-by-step explanation:
That's a triple I remember
Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour after consumption of 30 mL of ethanol (corresponding to two alcoholic drinks). (Round your answers to two decimal places.)
t (hours) 1.0 1.5 2.0 2.5 3.0
C(t) (mg/mL) 0.35 0.22 0.16 0.1 0.09
Required:
Find the average change of C with respect to t over each time interval.
a. [1.0, 2.0]
b. [1.5, 2.0]
c. [2.0, 2.5]
d. [2.0, 3.0]
The average change of C with respect to t over each time interval is given below:a. [1.0, 2.0]
Average change in C with respect to t is -0.1. It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.16-0.35)/(2-1)]b. [1.5, 2.0]:
Average change in C with respect to t is -0.08. It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.16-0.22)/(2-1.5)]c. [2.0, 2.5]:Average change in C with respect to t is -0.02.
It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.1-0.16)/(2.5-2.0)]d. [2.0, 3.0]:Average change in C with respect to t is -0.005. It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.09-0.1)/(3.0-2.0)]
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Point A is located at (5,-2) It is translated along (-8,-3) and then rotated reflected across the line y=x. What are the coordinates of its image after the transformations?
The coordinates of the image point C after the given transformations are (-5, -3).
What is the coordinate point called?
The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0).
To apply the given transformations to point A, we need to follow these steps:
Translate the point along vector (-8, -3) to get a new point B.
Reflect the point B across the line y=x to get the final image point C.
Let's first translate point A to get point B. To do this, we add the components of the translation vector to the coordinates of point A:
B = A + (-8, -3)
B = (5, -2) + (-8, -3)
B = (-3, -5)
So, point B is located at (-3, -5).
Next, we reflect point B across the line y=x to get the final image point C. To do this, we switch the x and y coordinates of point B:
C = (y, x)
C = (-5, -3)
Therefore, the coordinates of the image point C after the given transformations are (-5, -3).
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The tax on a bicycle costing $400 is $32 how much will the tax be on a bicylce costing $700 if the tax remains the same
The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.
To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.
tax rate = (tax / cost of bicycle) x 100%
tax rate = (32 / 400) x 100%
tax rate = 8%
Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.
tax on $700 bicycle = (tax rate / 100) x cost of bicycle
tax on $700 bicycle = (8 / 100) x $700
tax on $700 bicycle = $56
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How do you simplify it? I know the answer is 6_/6p but I don’t really know *how* to get there.
Answer:
The answer is
\(6 \sqrt{6p} \)Step-by-step explanation:
\( \sqrt{216p} \)First of all factor out the perfect square
From the question the perfect square is 36
We have
\( \sqrt{36 \times 6p} \)The root of a product is equal to the product of the roots of each factor
That's
\( \sqrt{36 \times 6p} = \sqrt{36} \times \sqrt{6p} \)Simplify
\( \sqrt{36} = 6\)So we have
\(6 \times \sqrt{6p} \)We have the final answer as
\(6 \sqrt{6p} \)Hope this helps you
Range of g(x)=3 square root of x
The range of the function g(x) is given as follows:
[0, ∞).
How to obtain the domain and range of a function?The domain of a function is obtained as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is obtained as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:
[0, ∞).
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What’s the domain of this relation (-1,5) , (0,4), ( 1,2) , (3,-2)
Answer:
{-1, 0, 1, 3}
Step-by-step explanation:
A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.
On the occasion of Teej, the principal of a school organized a Teej program for her female staffs. She distributes 90 bangles and 108 sweetse the staffs including herself. If there are 20 male staffs in the s school meximum number of staffs of her school
There is no valid solution. This implies that the information provided is contradictory or inconsistent. Therefore, we cannot determine the maximum number of staff members in the school based on the given information.
To find the maximum number of staff in the school, we need to determine the number of female staff members. We are given that the principal distributed 90 bangles and 108 sweets to the female staff members, including herself. Let's denote the number of female staff members (excluding the principal) as F.
We can set up the following equations based on the information given:
The number of bangles distributed to female staff members is 90.
The number of sweets distributed to female staff members is 108.
The total number of staff members, including both female and male staff members, is F + 1 (including the principal) + 20 (male staff members).
From equation 1, we have:
90 = F
From equation 2, we have:
108 = F
Since both equations 1 and 2 are equal to F, we can equate them:
90 = 108
This equation is not true.
It's important to note that if the given information was consistent and solvable, we could find the maximum number of staff members by summing the number of female staff members (F), the principal (1), and the male staff members (20)
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Use the drop-down menus to complete each equation so the statement about its solution is true. No Solutions 6x – 3x + 4 – 2x ={ ? } x + (?)
One Solution 6x – 3x + 4 – 2x =(?) x + [ ? )
Infinitely Many Solutions 6x – 3x + 4 – 2x =(?)x +?
fill in the question marks
Answer:
Simplify the expression.
x
+
4
Step-by-step explanation:
ST lie on the coordinate plane with S located at (3,2). the midpoint of ST is Z(3,5). Can the location of T be determined
Answer:
T(3, 8)
Step-by-step explanation:
Yes, it can.
Use the midpoint formula with points S and Z, and solve for point T.
M( (x_1 + x_2)/2 , (y_1 + y_2)/2 )
Z(3, 5) = ( (3 + x)/2 , (2 + y)/2 )
(3 + x)/2 = 3
3 + x = 6
x = 3
(2 + y)/2 = 5
2 + y = 10
y = 8
T(3, 8)
in the number 25,308, which digit is in the ten thousands place?
Answer:
It is 2 which represents 20,000
What is the slope of the line that passes through the points (−6,−4) and (-12, -4) ?
Answer:
0
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ].
-4-(-4)/-12-(-6)
0/-6
Since the numerator is 0, the slope is 0.
Best of Luck!
a sequence is ---select--- sequence when the first differences are all the same nonzero number.
A sequence is arithmetic sequence when the first differences are all the same non-zero number.
An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.
As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.
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use a trigonometric substitution to evaluate integral root y^2-25/y dy, y>5
The integral evaluates to 5(tan(arcsec(y/5)) - arcsec(y/5)) + C.
What is integral?
The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.
To evaluate the integral ∫(√(y² - 25))/y dy, where y > 5, we can use a trigonometric substitution. Let's substitute y = 5sec(θ).
First, we'll find the derivative of y with respect to θ:
dy/dθ = 5sec(θ)tan(θ)
Next, we'll express the integral in terms of θ and dθ:
∫(√(y² - 25))/y dy = ∫(√((5sec(θ))² - 25))/(5sec(θ)) * (5sec(θ)tan(θ)) dθ
= ∫√(25sec²(θ) - 25) tan(θ) dθ
= ∫√(25(tan²(θ) + 1) - 25) tan(θ) dθ
= ∫√(25tan²(θ)) tan(θ) dθ
= ∫5tan(θ) tan(θ) dθ
= 5∫tan²(θ) dθ
Now, we'll use the trigonometric identity 1 + tan²(θ) = sec²(θ) to simplify the integral:
∫5tan²(θ) dθ = 5∫(sec²(θ) - 1) dθ
= 5(∫sec²(θ) dθ - ∫dθ)
= 5(tan(θ) - θ) + C,
where C is the constant of integration.
Finally, we'll substitute back y = 5sec(θ) to express the solution in terms of y:
∫(√(y² - 25))/y dy = 5(tan(θ) - θ) + C
= 5(tan(arcsec(y/5)) - arcsec(y/5)) + C.
Hence, the integral evaluates to 5(tan(arcsec(y/5)) - arcsec(y/5)) + C.
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Cylinder A has a volume of 6 cubic units, and a height of 3 units. Cylinder B has the same base area and height,
but its slant height is 4 units. What is the volume of cylinder B?
Answer: 6
Step-by-step explanation: