Evaluate: 54.25÷6.2−3.8

Answer:

x = 5

Step-by-step explanation:

Change "minus a negative" to "plus a positive"

x - (-3) = 8

x + 3 = 8

Next, subtract 3 from both sides.

x + 3 - 3 = 8 - 3

x = 5

Check it!

x - (-3) = 8

5 - (-3) = 8

5 + 3 = 8

8 = 8 Check!

The sum of the given series is 50

The summation notation or sigma notation is used to simplify the writing of long summation into a single formula.

The given series in sum notation is:

       [tex]\sum\limits^5_{n=1} {(3n+1)}[/tex]

Substitute n = 1 ...5 into the nth term formula inside the sum notation:

a(1) = 3 . (1) + 1 = 4

a(2) = 3. (2) +1 = 7

a(3) = 3. (3) +1 = 10

a(4) = 3. (4) +1 = 13

a(5) = 3. (5) +1 = 16

Hence, the series:

    4 + 7 + 10 + 13 + 16

We can evaluate the sum directly by adding all the terms:

S(5) = 4 + 7 + 10 + 13 + 16 = 50

Or we can also use the sum formula of an arithmetic series:

S(n) = n/2 [a(1) + a(n)]

For n = 5

S(5) = 5/2 (4 + 16)

S(5) = 5/2 . 20 = 50

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The lengths 12, 16, 10, 5, and 2 of the sides, AP, DQ, CS, PQ, and QR respectively, using the triangle proportionality theorem, gives the area of trapezoid BRSC as 40 square units.

The triangle proportionality theorem states that a line parallel to a side of a triangle and also intersects the other two sides, it divides the two sides proportionally.

Based on the theorem, where the other two sides are perpendicular, the parallel side divides the two sides equally.

The given parameters are;

The figure represented by ABCD = A parallelogram

The lengths of the sides of the figure are;

AP = 12

DQ = 16

CS = 10

PQ = 5

QR = 2

Required: The area of figure BRSC

Solution;

Given that ABCD is a parallelogram, we have;

AD = BC (definition of a parallelogram)

Using the triangle proportionality theorem, we have;

PQ = RS = 5 (segments bounded by equidistant parallel lines)

DQ - CS = AP - BR = 16 - 10 = 6 (Parallel vertical lines intersected by parallel lines at different heights)

AP - BR = 6

BR = 12 - 6 = 6

The area, A, of trapezoid BRSC is therefore;

A = RS × (BR + CS)/2

Which gives;

A = 5 × (6 + 10)/2 = 40

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Answer:

let 3A5A be equal to 15

3A5A=15

A=1

Answer:

a = 5

Step-by-step explanation:

3555/15 is 237 which means it is divisible

The volume of the larger cylindrical can of tuna with radius 5.2 centimeters is 419.6 cubic centimeters.

Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:

height of A / height of B = radius of A / radius of B

Using this scale, if the larger and similar can of tuna has a radius of 5.2 centimeters, and the small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters, then:

radius of larger cylinder / radius of smaller cylinder = 5.2 cm/4cm = 13/10

height of larger cylinder / height of smaller cylinder = 13/10

height of larger cylinder = 13/10 (3.8 cm)

height of larger cylinder = 4.94 cm

Solving for the volume of the larger can using the formula for the volume of cylinder:

V = πr^2h

V = π(5.2 cm)^2(4.94 cm)

V = 419.6464068 cubic centimeters

Rounding off to the nearest tenth.

V = 419.6 cubic centimeters

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Answer:

1.48

Step-by-step explanation:

Redefined the logarithm into its decimal form within the base.

Hope this helps.

Answer:

x= negative goes on the out side of it 15 over 4

Answer:

c=0/0

Step-by-step explanation:

Let's solve for c.

x−c

c−x

=−1

Step 1: Multiply both sides by c-x.

−c+x=−c+x

Step 2: Add c to both sides.

−c+x+c=−c+x+c

x=x

Step 3: Add -x to both sides.

x+−x=x+−x

0=0

Step 4: Divide both sides by 0.

0

0

=0/0

c= 0/0

Answer:

Step-by-step explanation:

False for all value of x, because "x" should not be equal "c"

The coordinates of the point P is P(x, y) = (- 1, - 10 / 7). (Correct choice: B)

In this problem we find the coordinates of two points on Cartesian plane, of which we must determine the location of a third point by using a formula based on a weight average-like formula:

P(x, y) = (4 / 7) · A(x, y) + (3 / 7) · B(x, y)

P(x, y) = (4 / 7) · (- 4, 2) + (3 / 7) · (3, - 6)

P(x, y) = (- 16 / 7, 8 / 7) + (9 / 7, - 18 / 7)

P(x, y) = (- 7 / 7, - 10 / 7)

P(x, y) = (- 1, - 10 / 7)

The coordinates of the point P is P(x, y) = (- 1, - 10 / 7).

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By substitution, the solution of the system of equations, 3u + 8 = 4v and 24v = 6 - 3u, is (u , v) = (-2 , 1/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in u and v,

3u + 8 = 4v     (equation 1)

24v = 6 - 3u     (equation 2)

Using the first equation, find the value of one variable, lets say u, in terms of the other.

3u + 8 = 4v     (equation 1)

3u = 4v - 8

u = (4v - 8)/3

Substitute the value of u to the second equation.

24v = 6 - 3u     (equation 2)

24v = 6 - 3[(4v - 8)/3]

24v = 6 - (4v - 8)

24v = 6 - 4v + 8

Combining all terms containing the variable v on one side and the constants on the other side of the equality, and solve for v.

24v = 6 - 4v + 8

24v + 4v = 6 + 8

28v = 14

v = 1/2

Substitute the value of v in the equation for u and solve for u.

u = (4v - 8)/3

u = [4(1/2) - 8]/3

u = (2 - 8)/3

u = -6/3

u = -2

Hence, the solution of the given system of equations is (u , v) = (-2 , 1/2).

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Answer:

3a² √2a

(o´▽`o)ﾉ xx

The critical value is [tex]5[/tex] for the statistical test to test the mean child mortality rate for countries in Africa and the mean child mortality rate for countries in South Asia.

The child mortality rate or under age as five mortality rate tells that the child is dying during birth timing or exactly at the age of five. Globally million kids are dying at the age of five due to diseases like pneumonia or diarrhea or malaria etc. It is a big concern as well as a matter of responsibility for the child's survival at the age of five.

Many places in the world suffer from these problems and countries with low income ranges have a burden of child mortality. This problem is unevenly distributed throughout the world. Child survival is a constrained resource nowadays. The maximum child death is in sub Saharan Africa due to severe acute malnutrition.

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The equation in slope-intercept form for the line that passes through (-12,3), perpendicular to y = -(2/3)x-11 is y = (3/2)x + 21.

The slope intercept form of a line is:-

y = mx + b

Where:-

m represents the slope of a line

b represents the y-intercept of a line

x and y represent the ordered pairs (x,y) throughout a line

We are given the line y = - (2/3)x-11 is perpendicular to the line whose equation we have to find.

Hence,

slope of the line*(-2/3) = -1

slope of the line, m = 3/2

Also, (-12,3) passes through the line,

Hence,

3 = (3/2)*(-12) + b

3 = -18 + b

b = 21

Hence, the equation of the line in slope intercept form is y = (3/2)x + 21.

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Answer:

y = 8

Step-by-step explanation:

x = 4 is the equation of a vertical line parallel to the y- axis.

A perpendicular line will be a horizontal line with equation

y = c ( where c is the value of the y- coordinates the line passes through )

the line passes through (- 9, 8 ) with y- coordinate 8 , then

y = 8 ← equation of perpendicular line

The probability that the coin lands heads up and the number rolled is a 6 is 1/12.

Given that a die is rolled and a coin is tossed.

We have to find the probability that the coin lands heads up and the number rolled is a 6.

Probability of getting heads in tossing a coin = 1/2

Probability of getting 6 in rolling a die = 1/6

The event of tossing a coin and rolling die are independent.

Hence,

Probability that the coin lands heads up and the number rolled is a 6 =

Probability of getting heads in tossing a coin * Probability of getting 6 in rolling a die =  (1/2)*(1/6) = 1/12.

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Answer:

Yes, 3 + (-4) is the same as -4 + 3.

Step-by-step explanation:

When doing addition problems such as this, the order of the numbers does not matter, even when negative numbers are included.
For example, 1 + 2 or 2 + 1 would equal 3.

3 + (-4) = -1
-4 + 3 = -1

Hope this helped you! Let me know if you need more clarification. :)

Answer:

if I can't explain in one line, then I will include the steps in the explanation.

Step-by-step explanation(Q3):

[tex]3^2-\left(5-3\right)^3+6\\5-3=2\\3^2-2^3+6\\3^2=9\\9-2^3+6\\2^3=8\\9-8+6\\9-8=1\\1+6\\1+6=7\\=7[/tex]

Hope it helps!

Answer: 1/10

Step-by-step explanation: -2/5+1/2=0.1

If we convert 0.1 into a fraction, it becomes 1/10.

Answer:

1/10 is the answer

The quotient of the decimal number 89.904 divided by 34 will be 2.65.

In mathematics, the sum obtained by diluting two numbers is known as a quotient. In mathematics, the word "quotient" is widely used, and it is sometimes referred to as the integer part of a division, a fraction, or a ratio.

The decimal numeral system is widely used to express both integer and non-integer numbers.

Given numbers are 89.904 and 34. The quotient will be calculated as below:-

Quotient = 89.904 / 34

Quotient = 2.65

Therefore, the quotient of the decimal number 89.904 divided by 34 will be 2.65.

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The amount of gas he would have in the tank after 3 hours is 8 gallons.

The gas left after tt hours is 11 - tt.

In order to determine the amount of gas that would be left in the tank, the amount of gas used would have to be subtracted from the initial amount of gas in the car.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.

Amount of gas left = initial amount of gas - (gas used per hour x number of hours travelled)

11 - tt

11 - 3 = 8 gallons

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Answer:

90%

Step-by-step explanation:

The number of units manufactured at a cost of $8900 will be 104 units.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the cost, C(x), for manufacturing x units of a certain product is given by

C(x) = x² - 19x + 60

The number of units manufactured at a cost of $8900 will be given by factorization.

x² - 19x + 60 = 8900

x² - 19x - 8840 = 0

x² - 104x + 85x - 8840 = 0

x(x - 104) + 85(x - 104) = 0

(x - 104)(x + 85) = 0

x = 104, -85

The number of units manufactured at a cost of $8900 will be 104 units.

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The  radius of the new sphere of dough is 5.3368

In the given statement is :

Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough.

To find the approximate radius of the new sphere of dough

V 1 = 4/2 · 3³ π = 108/3 π

V 2 = 4/3 · 5³ π = 500/3 π

The new sphere:  V = V 1 + V 2 = 608/3 π

4/3 r³ π = 608/3 π  / : π/3

4 r³ = 608

r³ = 608 : 4 = 152

r = ∛152

r = 5.3368 cm

Hence, The  radius of the new sphere of dough is 5.3368

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Answer:

Image result for Use the Hypotenuse Theorem

The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want the height drawn on each triangle corresponding to the base shown.

The height of a triangle is the perpendicular distance from the base to the opposite vertex. The point at which the height segment meets the base may or may not lie on the triangle.

The height segments for the two given triangles are shown in the attachment.

__

Additional comment

As this problem suggests, any side of a triangle may be designated the "base."

The height segment is also called an altitude. When all three altitudes are extended until they coincide, the point at which they meet is called the "orthocenter" of the triangle.

The orthocenter of an acute triangle lies inside the triangle. For a right triangle, it lies at the right-angle vertex. For an obtuse triangle, the orthocenter is outside the triangle.

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Step-by-step explanation:

Let us start with Frodo's breakfast. He starts eating a quarter of the porridge. Let us say the porridge is 100 spoons, to make dividing easier. After Frodo we have [tex]\frac{3}{4}[/tex] left of the original bowl; we are left with 75 spoons.

100 - [tex]\frac{1}{4}[/tex] = 100 - 25 = 75

Next, comes Sam's breakfast. He eats 75 - [tex]\frac{1}{4}[/tex] = 75 - 18.75 = 56.25 spoons left.

Next, we have Pippin's breakfast. He eats 56.25 - [tex]\frac{1}{4}[/tex] = 42.1875 spoons.

Lastly, we have Merry's breakfast. He eats 42.1875 - [tex]\frac{1}{4}[/tex] = 31.640625 spoons.

Now, we know we have 31.640625 spoons left. However, we need to know what fraction this is out of the original porridge bowl. So, we do:

31.640625 * 100 = 3164.0625 * 1 = 3164.0625

3164.0625% of the bowl remaining!

What a yummy breakfast!