According to the Pythagoras theorem, the value of the other leg is, 15.7 cm
Pythagoras theorem:
Pythagoras theorem defines that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.
Here we need to find the measure of the other leg and round off it to nearest tenth.
Though the given question, we know that the value of
Hypotenuse = 16 cm
one leg = 3cm,
Then let us consider the length of the other leg as x.
So, according to the Pythagoras theorem,
It can be calculated as,
=> hypotenuse² = one leg² + other leg²
=> 16² = 3² + x²
=> 256 = 9 + x²
Here we need the value of x, so it can be rewritten as,
=> 247 = x²
=> x = √247
When we take square root for 247, then we get the value of x as,
=> x = 15.716
When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.
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Describe the end behavior of the function graphed below.
The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3), and the minima of the given function at the point (-3, -12), and maxima at point (3,2).
What is a graph?A graph can be defined as a pictorial representation or a diagram of any function that represents data or values.
According to the given graph,
We can see that the function is decreasing at the interval (-∞, -3), then the function is increasing at the interval (-3, -1), then the function is decreasing at the interval (-1, 1), the function is increasing at the interval (1, 3), and the function is decreasing at the interval (3, ∞).
The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3).
Thus, the minima of the given function at the point (-3, -12), and maxima at point (3,2).
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Suppose the math club is going on a field trip. Members will be riding in vans that will hold 7 people each including the
driver. More than 28 people will be going on the field trip. Do not put spaces in your answers.
Write an inequality to model this situation using V as the variable.
Solve the inequality.
What is the least number of vans needed to make the trip?
Answer: 4v so this would be the correct answer.
Which expression is NOT equivalent to 6 × 14?
6 × (10 + 4)
6 × 7 + 6 × 7
6 × 10 + 6 × 4
6 × (10 × 40)
Answer: 6 × (10 × 40)
Answer:
6 × (10 × 40)
Step-by-step explanation:
6 × 14 = 84
6 × (10 + 4) = 6 × 14 = 84
6 × 7 + 6 × 7 = 42 + 42 = 84
6 × 10 + 6 × 4 = 60 + 24 = 84
6 × (10 × 40) = 6 × 400 = 2400
Show that diagonal EG is a line of symmetry for rhombus EFGH.
The diagonal EG is a line of symmetry for rhombus EFGH
A rhombus is a quadrilateral with equal sides. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.
Given rhombus EFGH
We have to prove that diagonal EG is a line of symmetry for rhombus EFGH
According to the property of the rhombus
Four sides of EFGH are equal
So EF = EH
FG =HG
Meanwhile EG =EG(common side)
So triangle EFG = triangle EHG
The diagonal EG is a line of symmetry for rhombus EFGH
Therefore the diagonal EG is a line of symmetry for rhombus EFGH
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At a particular restaurant, each mini hotdog has 90 calories and each pizza roll has 50 calories. A combination meal with pizza rolls and mini hotdogs is shown to have 860 total calories and 6 more pizza rolls than mini hotdogs. Write a system of equations that could be used to determine the number of mini hotdogs in the combination meal and the number of pizza rolls in the combination meal. Define the variables that you use to write the system.
The number of mini hotdogs in the combination meal is 4.
The number of pizza rolls in the combination meal is 10.
The variables that you use to write the system are x and (x + 6).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation
We have,
Number of hot dogs = x
Number of pizza = x + 6
Hot dogs calories = 90
Pizza calories = 50
Now,
90x + 50(x + 6) = 860
Solve for x.
90x + 50x + 300 = 860
140x = 860 - 300
140x = 560
x = 560/140
x = 4
We can cross-check.
90 x 4 + 50 x 10 = 860
360 + 500 = 860
860 = 860
Thus,
The number of hot dogs is 4.
The number of pizzas is 10.
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marking brainliest!! help much needed!
Find the missing value so that the line passing through the 2 points has the given slope.
(12, -12) and (7, y); slope: -3
a. 3
b. 18
c. -15
Step-by-step explanation:
y = 3
Step-by-step explanation:
Calculate the slope between the 2 points using the slope formula, then equate to - 3
m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }
x
2
−x
1
y
2
−y
1
with (x₁, y₁ ) = (12, - 12 ) and (x₂, y₂ ) = (7, y )
m = \frac{y-(-12)}{7-12}
7−12
y−(−12)
= \frac{y+12}{-5}
−5
y+12
= - 3 ( multiply both sides by - 5 )
y + 12 = 15 ( subtract 12 from both sides )
y = 3
Answer:
Step-by-step explanation:
help me solve this problem
The value of GK = 18.6, GM = 14.5 AND JZ = 19.9.
From the figure:
MZ is a perpendicular bisector of ∆GHJ.
GM = MJ
GM = 14.5
KZ is a perpendicular bisector of ∆GHJ.
GK = KH
GK = 18.6
Z is the circumcenter of ∆GHJ.
JZ = GZ
JZ = 19.9
Therefore the value of GK = 18.6, GM = 14.5 AND JZ = 19.9.
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How does T critical value calculator work?
The working of T critical value calculator is explained
What is t test?
t test is the test used if the sample standard deviation is known and population standard deviation is unknown.
t test is used if the sample standard deviation is known and population standard deviation is unknown.
Here, t value is calculated by the formula
[tex]t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]\bar{x}[/tex] = mean of the sample
[tex]\mu[/tex] = mean of the population
s = standard deviation of sample
n = Number of samples
Now, with the help of degree of freedom (n - 1) and the level of significance, the critical value of t is to be noted from the t table. Let it be [tex]t_{critical}[/tex]
if the value of t lies between [tex]-t_{critical}[/tex] and [tex]+t_{critical}[/tex] then the null hypothesis is accepted, otherwise the null hypothesis is rejected.
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find the area of a rectangle 73 cm by 26 cm Help me please? I'm so confused?
Answer:
1898
Step-by-step explanation:
Multiply both numbers together to find the area.
Suraj took a slice of pizza from the freezer and put it in the oven. The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is graphed. How long was each increase by 4 degrees Celsius?
A.) 1/2
B.) 1 Minute
C.) 1/4
D.) 1/3
The time taken for the increase in temperature by 4 degrees Celsius is 1/2 minute.
Suraj took a slice of pizza from the freezer and put it in the oven. The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is given in the form of a graph. The coordinates of the points through which the line passes are (2, 10) and (4.5, 30). We can find the slope of the straight line. If the coordinates of two points are (x1, y1) and (x2, y2), then the slope of the passing line is given as below.
m = (y2 - y1)/(x2 - x2)
m = (30 - 10)/(4.5 - 2)
m = 20/2.5
m = 8
This means there is an increase of 8 degrees in temperature in one minute. We need to calculate the time taken for a 4-degree increase in temperature.
m = Δy/Δx
8 = 4/Δx
Δx = 4/8 = 1/2
Hence, the increase in temperature by 4 degrees Celsius took half a minute.
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Which fraction is the smallest?
3/5 1/2 2/3 4/7 3/8
-7(-4w - x + 5) Use the distributive property to remove the parentheses
Answer: -28w + 7x -35
Step-by-step explanation:
[tex]-7(-4w -x +5)\\\\= -7*-4w + (-7)*(-x) + (-7)*5= -28w + 7x -35[/tex]
Answer:
28w+7x-35
Step-by-step explanation:
When one function undoes or reverses another function, what can you say about the
functions?
Answer:
An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
Step-by-step explanation:
could someone please help me? ASAP!
Answer:
$1.2
Step-by-step explanation:
If the tax is 3% then we will have to multiply the price($40) by .03
40*.03= 1.2
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
The rate of change is the slope. See the picture. The blue line (Function B) is steeper than the red line (Function A).
Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.54.54, point, 5 milliliters per second. After 171717 seconds, 148.5148.5148, point, 5 milliliters of slushy remained.
How much slushy was originally in the cup?
milliliters
How long did it take Mariana to drink all the slushy?
seconds
The amount of slushy that was originally in the cup is 225 milliliters and the time it took Mariana to drink all the slushy is 50 seconds.
How to find the original quantity?Total quantity she took
Total quantity = 4.5 × 17
Total quantity = 76.5 milliliters
Original quantity = 148.5 + 76.5
Original quantity = 225 milliliters
b. Time taken to drink all
Time =225 milliliters /2.5
Time = 50 seconds
Therefore original quantity 225 milliliters and the time is 50 seconds.
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make x the subject of 4(x-3)/a
The rearranged form of equation 4(x-3)/a=y will be x=ay+3.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the expression is, 4(x-3)/a=y
First, we open the bracket to make x the variable in the equation.
4x - 12/a = y
4x - 12 = ay
4x = ay + 12
x = ay + 12/4
x = ay + 3
Thus, the rearranged form of equation 4(x-3)/a=y will be x=ay+3.
The question is incomplete,
The complete question is"Rearrange to make x the subject of 4(x-3)/a=y:
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cesium 134 decays exponentially. the half life of cesium-134 is 2 years. suppose we have a 50mg sample. after how long after how long will only a 10 mg sample
Cesium would remain 10g after 2 years in 9.55 gram.
Define exponential decay.A process known as exponential decay is when a quantity diminishes over time at a pace that reduces proportionally as the quantity shrinks. The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
Given,
Cesium 134 decays exponentially. the half life of cesium-134 is 2 years.
The half-life of cesium is approximately 30 years.
The formula for half-life decay is A = P(1/2)t/d.
The half life is D. A Equals 9.55 gram when 10 gram and 2 years are entered into the equation.
Cesium would remain 10g after 2 years in 9.55 gram.
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Genesis owns a small business selling clothing. She knows that in the last week 6
customers paid cash, 66 customers used a debit card, and 44 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with
something other than cash as a percent to the nearest whole number.
The probability of the next customer paying with a debit or credit card other than cash is =94.82%
We have given,
Genesis owns a small business selling clothing.
She knows that in the last week 6 customers paid cash, 66 customers used a debit card, and 44 customers used a credit card.
we are asked to determine the probability that the next customer will pay with something other than cash as a percent to the nearest whole number
P(A)= number of favorable outcome in event A divided by the total outcome in a sample space
customers will pay through debit or credit card other than cash.
last week of customers paid cash: 6
last week of customers paid w/ a debit card: 66
last week of customers paid w/ a credit card: 44
Therefore, 6+66+44= 116
=110/116
=0.9482
= 94.82% is the probability that the next customer will pay with
something other than cash as a percent to the nearest whole number.
Hence we get the required answer.
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is clinical prediction the fairest way to combine assessment information about job applicants, or are the other methods (unit weighting, rational weighting, and multiple regression) more fair?
clinical prediction is not the fairest way to combine assessment information about job applicants, but the other methods (unit weighting, rational weighting, and multiple regression) are more fair
Clinical prediction appears to have a serious shortcoming in terms of overall fairness for applicants because it is a subjective process of bringing information and hence clinical prediction is not the fairest way to combine assessment information about job applicants .
unit weighting is the simple method which add scores of each candidate at each level of assessment in order to arrive at a total score
Thus the other methods (unit weighting, rational weighting, and multiple regression) are more fair
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A shopper bought a watermelon,a pack of napkins,and some paper plates. In his state, there is no tax on food. The tax rate on non-food items is 15 percent. The total for the three items he bought was $8.25 before tax, and he paid $0.19 in tax. How much did the watermelon cost?
Answer:
Step-by-step explanation:
the question is about 15% tax equaling 19 cents. So what amount of principle would be needed to make 19 cents worth of tax.
.19/.15=1.26666666
round up to $1.27 since we don't have parts of pennies for money.
8.25-1.27=$6.97 for the watermelon.
Scientists have calculated that the diameter of Himalia, one of Jupiter's moons, is 20 times smaller than the diameter of Earth's moon, which is 3480 km. What is the diameter of Himalia?
Find a number which is increased by 12 is two times its opposite.
N = _____
Final equation: ______
The number which when increased by 12 is two times its opposite. is
N = -4
final equation N + 12 = -2N
What is additive inverse?Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.
To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.
The problem says
N + 12 = -2N
N + 2N = -12
3N = -12
N = -4
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Pls help, if multiple people answer this, I’ll give someone brainliest :D
Answer:
B . 72 you have to skip count by 12
C . 18 because 54 divide by 3 is 18 because they frame 3 houses in one week
Sorry I tried to do the rest but got confused I hope this helps u
Step-by-step explanation:
Can someone please explain this to me my exams in one day
The rate of interest half yearly is 8.25 and monthly is 1.375%.
In the given question we have to find the effective rate of intereset, if a amount of money is borrowed an interest rate of 16.5% p.a. and is compounded.
The interest rate annually = 16.5%
(a) We have to calculate rate of interest half yearly.
In a half year have 6 months and in total have 12 months. So their is rate of interest for 2 times.
So the rate of interest half yearly = 16.5%/2
The rate of interest half yearly = 8.25%
(b) We have to calculate rate of interest monthly.
As we know that in a year have 12 months.
So the rate of interest monthly = 16.5%/12
The rate of interest monthly = 1.375%
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Find a formula for the nth term of the arithmetic sequence-2 -8 -14 -20…. (I did that already) but explain in detail using words on how you got the answer -6
The general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]
The given arithmetic sequence is -2, -8, -14, -20
The first term = a = -2,
The common difference = d = -8 -(-2) = -8 +2 = -6
The general term of the arithmetic sequence is given by
[tex]T_{n} = a + (n-1)d[/tex]
Now, putting the values of the first term and common difference in the general term.
[tex]T_{n} = -2 +(n-1) (-6)\\\\T_{n} = -2 -6n +6\\ \\T_{n} = -6n +4[/tex]
Hence, the general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]
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Write an algebraic expression for the verbal description.
The amount of acid in x liters of a 45% acid solution
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The algebraic expression for the verbal description:
The amount of acid in x liters of a 45% acid solution is
0.45x
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The amount of acid in x liters of a 45% acid solution.
This can be written as an expression as,
= 0.45x
We know that,
45% = 45/100 = 0.45
Thus,
The algebraic expression for the verbal description:
The amount of acid in x liters of a 45% acid solution is
0.45x
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if the test scores of a class of 35 students have a mean of 75.3 and the test scores of another class of 26 students have a mean of 65.6, then the mean of the combined group is
Answer:The mean of combined group is 71.12 kg
Step-by-step explanation:
Mean of 35 students test score=75.3
Total score of 35 students=mean×test score
=35×75.3
=2635.5
Mean of 26 students test score=65=65.6
Total score of 26 students= 26×65.6
=1705.6
Mean of combined group=(Total score of 35 students+Total score of 26 student ÷Number of total students
=(12635.5+1705.6)÷61
=71.16
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The combined group's average is 71.16.
Given;
If the average test score for one class of 35 students is 75.3 while the average test score for another class of 26 students is 65.6
Mean of 35 student's test scores = 75.3
The total score of 35 students is the mean * test score
=35 * 75.3 =2635.5
Mean of 26 student's test scores = 65.6
The total score of 26 students = 26 * 65.6 =1705.6
Mean of combined group = (Total score of 35 students + Total score of 26 students) / Number of total students
= (12635.5 + 1705.6) / 61
= 71.16
Hence, the mean of the combined group is 71.16
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Which angle is vertical to ∠EAD?
Please help!!!
Answer:
Step-by-step explanation:
Halie, find angle EAD.... see it? next think about the definition of vertical angles: each of the pairs of opposite angles made by two intersecting lines.
which angle is EAD an opposite pair of? ∠IAH looks like a good one.
Help pls
2 Answers and I can make brainliest whoever has the correct answer
Answer:
Step-by-step explanation:
Hope this helps :)
Answer:
1.01 g/cm³
Explanation:
The density of drink is 1.01 g/cm³ when 25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and 280 cm³ of carbonated water to make a drink with a volume of 320 cm³.
25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and
280 cm³ of carbonated water to make a drink with a volume of 320 cm³.
Let us find the mass of each drink mixed to make the new drink
mass = density × volume
mass of apple juice = 1.05 × 25
= 26.25 g
Mass of fruit syrup = 1.4 × 15
= 21 g
Mass of carbonated water = 0.99 × 280
= 277.2 g
Total mass of the drink = 26.25 g + 21 g + 277.2 g
= 324.45 g
Volume of the given drink = 320 cm³
Density of the drink = total mass of liquids/ volume
= 324.45g/320cm³
= 1.01 g/cm³
Thus, the density of drink is 1.01 g/cm³ when 25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and 280 cm³ of carbonated water to make a drink with a volume of 320 cm³.