The sixth term of the arithmetic progression is 94.
An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.
Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:
an = a + (n-1)d
We know that the sum of the first four terms is 14, so we can set up the following equation:
a + (a+d) + (a+2d) + (a+3d) = 14
We also know that the sum of the first eight terms is 108, so we can set up another equation:
a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108
Now we can use the first equation to substitute for the first four terms of the second equation:
14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108
This gives us:
a + 4d = 94
So the sixth term can be found by substituting n = 6 into the first formula:
a + (6-1)d = a + 5d = 94
Therefore, the sixth term of the arithmetic progression is 94.
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Kelly made fruit punch to erve at a party for her che team he mixed 1 2/5 liter of cranberry juice and 1 3/5 liter of pineapple juice together how much fruit punch did he make all together
Kelly pours 1/3 litre of fruit punch into each glass at a party for her chess team.
What does the division do?
divides left-hand operands into right-hand operands while performing a division operation in mathematics.
For instance, 4/2 = 2.
She combined the prescribed amounts of 1 2/5 litres of cranberry juice and 1 3/5 litres of pineapple juice.
The appropriate response to the aforementioned situation would be
⇒ 1 2/5 + 1 3/5
fractionalizing mixed numbers
⇒ 7/5 + 8/5
Consider the LCM in the previous equation.
⇒ (7 + 8)/5
⇒ 15/5
⇒ 3
She then divided the fruit punch equally among the nine cups.
3 litres of fruit punch must now be divided among 9 glasses.
3/9, therefore, equals 1/3 litres of fruit punch.
She, therefore, fills each glass with a third of a litre of fruit punch.
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9. Oscar's rectangular room has an area of 6x6y8 square units. If the width of Oscar's room can be represented by 2x³y2, which of the following represents the length of the room?
According to the given statement, 3x^3y^4 represents the length of the room.
What does word rectangle mean?Its length w is calculated using the formula h = A/w if you have an area A and a width w. Its length can be determined using the formula h = P/2w if you know its perimeter (P) and width (W). The length is given by h = (d2w2) if the diagonal d and width w are present.
Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.
The area of a square box is length x width, so that we can set up the calculation:
length x (2x³y²) = 6x6y8
To find the length of the court, we can divide both sides by 2x³y²:
length = (6x6y8) / (2x³y²)
so the length of a room is represented by 3x^3y^4
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The complete question is -
Oscar's rectangular room has an area of 6x^6y^8 square units. If the width of Oscar's room can be represented by 2x^3y^2, which of the following represents the length of the room?
(a)3x^2y^4
(b)3x^3y^4
(c)12x^9y^10
(d)12x^18y^16
What are the 7 types of symmetry?.
The seven types of symmetry are Euclidean, Reflectional, Point reflection, Rotational, Translational, Glide reflection, Helical and Double rotation symmetry.
In math the term symmetry is defined as one shape is exactly like the other shape when it is moved, rotated, or flipped.
Here we need to identify the seven types of symmetry.
As per the definition of symmetry here we have identified the types of symmetry as are possible for a geometric object depend on the set of geometric transforms available and on what object properties should remain unchanged after a transformation.
They are listed as follows, Euclidean symmetries, Reflectional symmetry, Point reflection and other involutivity isometries, Rotational symmetry, Translational symmetry, Glide reflection symmetry, Helical symmetry and Double rotation symmetry.
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How many times as intense as a standard earthquake is an earthquake measuring 3. 1 on the Richter scale?.
On the Richter scale is 1258.93 times as intense as a standard earthquake.
The Richter scale is a base-10 logarithmic scale, which means that each order of magnitude is 10 times more intensive than the last one. We have,
the an earthquake measuring 3. 1 on the Richter scale.
On Richter Scale, A = log(I/Iₛ)
here, A ---> amplitude
I --> intensity of earthquake
Iₛ ---> standard intensity of earthquake
As, A = 3.1
=> 3.1 = log(I/Iₔ)
Taking anti-logarithm both sides
=> 10³·¹ = I/Iₛ
=> 1258.93 = I/Iₛ
=> I = 1258.93 Iₛ
Therefore, the earthquake with measuring 3.1 on Richter scale is 1258.93 times as intense as a standard earthquake.
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What degree measure is equivalent to 7x/11?
Enter your answer, rounded to the nearest hundredth of a degree, in the box.
The degree measure is which is equivalent to [tex]\frac{7 \pi}{11}[/tex] is 114.54°.
What is meant by degree measure?The size of an angle is measured in terms of a unit of measurement. 1 degree is equivalent in magnitude to 1/360 of a whole rotation.
A rotational angle is said to have a measure of one degree, denoted by the symbol 1°, if it is (1/360)th of a revolution from the initial side to the terminal side. Radian scale. A unit circle's unit arc's centrally subtended angle is said to have a measure of 1 radian.
The radius of an arc divided by its length is known as the radian measure (r). Radian measure is a pure number that doesn't require a unit symbol because it is the ratio of one length to another.
Convert radians to degrees, multiply by 180/π, since a full circle is 360° or 2π radians.
= [tex]$ \frac{7 \pi}{11} \times \frac{180}{\pi}[/tex]
= [tex]$ \frac{7 }{11} \times 180[/tex]
=[tex]$ \frac{1260}{11}[/tex]
= 114.54°
Therefore, the correct answer is 114.54°.
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Full question:
How do you solve complex fractions and unit rates?.
A unit rate is a ratio that has a denominator of 1, such as miles per hour or dollars per item. To solve a complex fraction that involves a unit rate, you can follow the same steps as solving a regular complex fraction, but with an additional step to convert the final expression to a unit rate.
Factor the numerator and denominator of the complex fraction if possible.
Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator.
Simplify the resulting expression by combining like terms, if possible.
Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.
Divide the numerator by the denominator to get the unit rate.
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Been stuck on this for a while Please Help!
Answer:
x = 23°
Step-by-step explanation:
Sum of interior angle
(n - 2)180. note: the sides are 3
(3 - 2)180
(1)180
180°.
the value of x
31° + 3x° + 34° + 2x° = 180°
31° + 34° + 3x + 2x = 180°.
65° + 5x = 180°
5x = 180° - 65°
5x = 115°
5x/5 = 115/5
x = 23°
A store sells two brands of hand lotion. Brand X cost $3.25 for 5 fluid ounces. Brand Y cost $6.00 for 8 fluid ounces. How much less per fluid ounces does brand X cost then brand Y.
Based on the unit rate, Brand X costs $0.10 per fluid ounce less than Brand Y.
What is the unit rate?The unit rate refers to the ratio of one value to the whole.
The unit rate is the average of the values of the data set.
We can compute the unit rate by dividing the total value by the number of units.
The total cost of Brand X for 5 fluid ounces = $3.25
The unit cost of Brand X per fluid ounce = $0.65 ($3.25/5)
The total cost of Brand Y for 8 fluid ounces = $6.00
The unit cost of Brand Y per fluid ounce = $0.75 ($6.00/8)
The difference in the unit cost of Brand X and Brand Y = $0.10 ($0.75 - $0.65)
Thus, we can state that Brand Y costs more than Brand X per unit.
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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
always remember :
the sum of all angles in a triangle is always 180°.
so, in triangle EFD
180 = E + F + D = 37 + 105 + D
D = 38°
since we know that the combination (sum) of B and D is 90° (right angle),
B + D = 90
B + 38 = 90
B = 52°
and now we look at the triangle ABC and its angles to get A, which then in turn gets us I of the triangle A(BD)I.
180 = A + B + C = A + 52 + 83
A = 45°
and that means for A(BD)I
180 = A + (B + D) + I = 45 + 90 + I
I = 45°
FYI : that means that the total triangle is an isoceles triangle (both legs are equally long : AB = DI).
For the following equation, a. Write the value or values of the variable that make a denominator zero. These are the
restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.
For the given equation, the value of x = -21.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
For the given equation,
x ≠ ±3
On taking LHS,
⇒ [tex]\frac{5}{x+3} - \frac{2}{x-3}[/tex]
Taking LCM,
⇒ [tex]\frac{5(x-3) - 2(x+3)}{(x+3)(x-3)}[/tex]
⇒ [tex]\frac{5x - 15 - 2x - 6}{x^2 - 9}[/tex]
⇒ [tex]\frac{3x - 21}{x^2 - 9}[/tex]
On Comparing both sides,
⇒ [tex]\frac{3x - 21}{x^2 - 9} = \frac{4x}{x^2 - 9}[/tex]
⇒ 3x - 21 = 4x
⇒ x = -21
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A river guide conducts kayak and canoe tours along a scenic river. He charges a booking fee plus a variable rate depending on the number of passengers. The total cost for different numbers of passengers, including the initial fee, is shown on the graph.
Find and interpret the rate of change.
For the specified Data, the rate of change will be 8.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Kayak and canoe experiences are led by a river guide along a beautiful river. In addition to a booking fee and a variable tariff based on the number of passengers, he charges. The graph displays the total cost for various passenger counts, including the booking fee.
From general formula of rate of change = (y₂ - y₁)/ (x₂ - x₁)
in our case
y₂ = 72
y₁ = 56
x₂ = 4
x₁ = 2
thus rate of change = 16/2 = 8
Since A rate of change is the proportion of one quantity's change to another's change. There is a constant rate of change in linear relationships.
Therefore, The rate of change for the given equation will be 8.
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question 1: Harry has 4 ⅞ of a pizza and Mary has 1 ⅞ of a pizza. What is the estimated total of pizza they have together? ________
question 2: Sally has 5 ⅜ of a candy bar. She gives Omar 2 1/4 of the candy bar. Using benchmark fractions, determine how much of the candy bar Sally has left. Remember to estimate. _________
PLEASE HELP ASAP!!!
Answer:
[tex]6\frac{3}{4}[/tex] and [tex]3\frac{1}{8}[/tex]
Step-by-step explanation:
I don't know what benchmark fractions are but here's what I did
[tex]4\frac{7}{8} + 1 \frac{7}{8} = 5 \frac{14}{8} = 6 \frac{6}{8} or 6\frac{3}{4}\\5\frac{3}{8} - 2\frac{1}{4} = 5\frac{3}{8} - 2\frac{2}{8} = 3\frac{1}{8}[/tex]
The first question is straight forwards since the fractions have the same denominator, so its simply adding and simplification.
The second questions needs you to find a common denominator (8) and swap the fraction to that of 8 before subtracting
Each gift bag include a bouncy ball,ticker,and cookie. There are red,yellow,or green bouncy ball;iri,lily,or daiy ticker;and chocolate chip or oatmeal cookie. How many different gift bag could be made?
There are a probability of 6 different possible combinations of the gift bag with a bouncy ball, ticker, and cookie. These combinations include a red bouncy ball, an iri, lily, or daiy ticker, and either a chocolate chip or oatmeal cookie.
There are a total of 6 different possible combinations of the gift bag with a bouncy ball, ticker, and cookie. These combinations include a red bouncy ball, an iri, lily, or daiy ticker, and either a chocolate chip or oatmeal cookie. The red bouncy ball offers a vibrant and exciting option, while the iri, lily, and daiy ticker add a fun element of surprise. The two cookie options offer something delicious and comforting to enjoy. With all of the different combinations, there is something for everyone to enjoy! Each combination offers a unique and special gift bag that will be sure to bring a smile to anyone's face.
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The middle school dance team had 3 separate car washes on Saturday to raise money for new uniforms. The Main Street location raised $50 more than the Back Street location. The Washington Street location raised $50 more than half the amount raised at the Back Street location. How much did the dance team raise at each location if they raised a total of $600?
Answer:
Step-by-step explanation:
What are the solutions of the equation x4 5x2 36 0?.
The solutions of the equation x⁴ - 5x² - 36 = 0 are: x = -3, x = 3, x = 2i and x = -2i
Consider given equation x⁴ - 5x² - 36 = 0
Let us assume that x² = p
so, we get an equation,
p² - 5p - 36 = 0
Now we solve above quadratic equation.
p² - 5p - 36 = 0
using the Quadratic Formula where
a = 1, b = -5, and c = -36
[tex]\Rightarrow p=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow p = \frac{5\pm \sqrt{25+144} }{2}\\\\\\\Rightarrow p = \frac{5\pm \sqrt{169} }{2}\\\\\\ \Rightarrow p=\frac{5\pm 13 }{2}[/tex]
So, p = 9 and p = -4
But p = x²
So, x² = 9 OR x² = -4
For x² = 9, by taking square-root we get x = 3, x = -3
an equation x² = -4 has complex roots, x = 2i and -2i
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PLEASE HELPPP I REALLY NEED HELP
Answer: y = -2/3x+4
Step-by-step explanation:
negative slope
y intercept (0,4)
4th answer choice.
Answer:
D.
Step-by-step explanation:
It's really blurry but here's what I did
Pick two random points:
(0, 4) and (6,0) is what I picked personally.
Calculate slope: rise/run = [tex]\frac{0 - 4}{6 - 0} = \frac{-4}{6} = \frac{-2}{3}[/tex]
b is the y-int at 4 therefore your equation is [tex]y = \frac{-2}{3}x + 4[/tex]
(-4 + 9) x (8 - 3) Pls help asap
Answer:
25
Step-by-step explanation:
(-4 + 9) x (8 - 3)
= (5) x ( 5)
= 25
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(-4 + 9) \times (8 - 3)}\\\\\mathsf{-4 + 9 = \boxed{\frak 5}}\\\mathsf{8 - 3 = \boxed{\frak 5}}\\\\\mathsf{= (-4 + 9) \times (8 - 3)}\\\mathsf{= 5\times5}\\\mathsf{= 25}[/tex]
[tex]\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{25}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What is the y-intercept of 3x y =- 1?.
So, the y-intercept of the equation 3x + y = -1 is the point (0, -1).
The y-intercept of a linear equation in the form of y = mx + b is the point at which the line crosses the y-axis, which is the point (0, b). In the equation 3x + y = -1, the y-intercept is the point at which y = -1 and x = 0, which can be found by solving for y when x = 0:
3(0) + y = -1
y = -1
So the y-intercept of the equation 3x + y = -1 is the point (0, -1). This means that the equation of the line passes through the point (0, -1) on the Cartesian plane.
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a penguin walks 12 feet in 8 seconds at this rate:
how far can the penguin walk in 32 minutes?
how far can the penguin walk in 1 hour?
10-2 skills practice simplifying radical expressions
1. On simplifying the radical expression √28 the result is 2√7.
2. On simplifying the radical expression √40 the result is 2√10.
3. On simplifying the radical expression √72 the result is 6√3.
4. On simplifying the radical expression √99 the result is 3√11.
What is a radical expression?
Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.
The first radical expression is -
√28
Take the LCM of 28.
The LCM is obtained as - 2 × 2 × 7.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 2√7.
Therefore, the expression is 2√7.
The second radical expression is -
√40
Take the LCM of 40.
The LCM is obtained as - 2 × 2 × 2 × 5.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 2√10.
Therefore, the expression is 2√10.
The third radical expression is -
√72
Take the LCM of 72.
The LCM is obtained as - 2 × 2 × 2 × 3× 3.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 6√3.
Therefore, the expression is 6√3.
The fourth radical expression is -
√99
Take the LCM of 99.
The LCM is obtained as - 3 × 3 × 11.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 3√11.
Therefore, the expression is 3√11.
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What are the values of the three basic trigonometric ratios?.
The values of the three basic trigonometric ratios are Sine, Cosine, tangent.
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trig ratios, cosec, sec, and cot.
Sine: The ratio of the perpendicular to the hypotenuse is known as the sine ratio for every given angle. Sine of angle in the given triangle can be expressed as sin = AB/AC.Cosine: The proportion of an angle's base to its hypotenuse is known as the cosine ratio. The cosine of angle in the given triangle can be expressed as cos = BC/AC.Tangent: The ratio of the perpendicular to the base is known as the tangent ratio for every given angle. The tangent of angle in the given triangle can be expressed as tan = AB/BC.Learn more about trigonometric ratios;
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Please help for 10 points… I need this asap!!!
Answer: Is there an answer for 1/2? I'm not sure.
Step-by-step explanation: If you look at the line it's going up by one and over by 2.
To solve for slope (Rate of Change) you need to find the change and y over the change in x. (y2-y1) divided by (x2-x1) take two points on the graph that is touching a line.
Two points on your graph is (2,2), and (6,4). You would take the second y which is 4 and subtract it from the first y which is 2. (4-2 = 2). Then you take the second x (6) and subtract it from the second y (2). (6-2 = 4). Now that you have the change and x over the change in y. you divide the top number by the bottom number. If it's a fraction just simplify it. (2/4 = 1/2). I'm not that good at explaining but I hope this helps a lot!
Which model shows 2 + 0.4?
(use photo)
Answer:
B
Step-by-step explanation:
2 ÷ 0.4 = 5
----------------
find the product of 7/2 and 22
Answer:
98765
Step-by-step explanation:
What is the range of the function f x equals 3x to the power of 2+ 6x 8?.
Answer:[-11, ∞]
The range of the function f(x) = 3x2 + 6x - 8 is [-11, ∞].
Step-by-step explanation:
A well, whose diameter is 3 m, has been dug 21 m deep and the earth dug out is used to form an embankment 4 m wide around it. Find the height of the embankment.
Answer:
31.875 m
Step-by-step explanation:
We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.
The volume of the well is given by the formula for the volume of a cylinder:
V = πr^2h
where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).
V = π(1.5)^2(21) = 42.5π m^3
The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:
V = 1/3 πr^2h
where r is the radius of the base of the cone (4 m) and h is the height of the embankment.
V = 1/3π(4)^2h = 4/3πh m^3
Now we know that the volume of the embankment is equal to the volume of the well:
V = 42.5π m^3 = 4/3πh m^3
Then we can solve for h by dividing both sides by 4/3π:
h = 42.5π m^3 * 3/4π = 31.875 m
So the height of the embankment is 31.875 m.
A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?
*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*
Answer:
$54.01
Step-by-step explanation:
All you have to do is $300.00-$245.99 .
!!! 50 points !!!
Rug to place in the middle of his bedroom. He draws a diagram to show where he will place is rug. Part A: Sam needs to find the perimeter of his bedroom. Use the picture to write three expressions that represent the perimeter, in feet, of Sam’s room.
Part B: now, Sam wants to find the area of his bedroom. He says that he can find the area using the expression 40x + 12 square feet. Is he correct? If he is incorrect, how many square feet is he off by?
Part C: Sam’s friend Carla has a square a bedroom with side length 4x + 6. Compare the perimeter of Carla’s room to the perimeter of Sam’s room.
write an inequality whos solution is an empty set
Inequality 5 > 6 is an example of an inequality whose solution is an empty set.
What is inequality?
An inequality is a statement that compares two expressions using one of the following mathematical symbols: <, >, ≤, ≥, ≠. It shows the relationship between the values of the expressions, but unlike an equation, it does not show that the expressions are equal.
For example, the inequality 3x + 4 > 7 compares the value of the expression 3x + 4 to the value of 7. It shows that 3x + 4 is greater than 7 for all values of x.
An inequality that has an empty set as its solution is one that has no solutions. For example, inequality 5 > 6 is an example of an inequality whose solution is an empty set because it is impossible for any value of x to satisfy the inequality. Any value of x will be less than 6 so it is impossible for x to be greater than 6.
Hence, Inequality 5 > 6 is an example of an inequality whose solution is an empty set.
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Geometry
You randomly select 3 cards from a standard deck of 52 playing cards. What is the probability that all 3 cards are hearts when...
a. You replace each card before selecting the next card.
b. You do not replace each card before selecting the next card?
a. You replace each card before selecting the next card.
The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is also 13/52 or 1/4. And the probability of drawing a heart on the third draw is also 13/52 or 1/4.
Since the events are independent, we can multiply the probability of each event to find the probability that all three cards are hearts: (1/4) * (1/4) * (1/4) = 1/64.
b. You do not replace each card before selecting the next card.
The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is 12/51 since we already drew a heart before, the total number of cards left in the deck is 51. The probability of drawing a heart on the third draw is 11/50 since we already drew 2 hearts before, the total number of cards left in the deck is 50.
The probability that all three cards are hearts is (1/4) * (12/51) * (11/50) = 0.0217 or approximately 2.17%.
It's important to note that in the first case the probability of drawing a heart on the second and third draw is still 1/4 because we are replacing the cards back before drawing the next one, so all 52 cards are available again. While on the second case, we don't replace the cards back and that's why the probability of drawing a heart on the second and third draw is different.Answer:
Step-by-step explanation:
