The rate of flow of syrup from the tree will be in mixed fraction form, equal to 1 1/2.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data mentioned in the question,
The amount of syrup obtained from the tree = 3/4 cup
The time is taken to fill 3/4 cup = 1/2 hour
Then, the rate of flow of syrup will be,
(3/4) ÷ (1/2)
3/4 × 2/1
= 6/4 = 3/2
It can also be written in mixed fraction form,
= 1 1/2
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When I double my number and add seven, I get what number?
Find the sum and product of the roots. 3x 2 - 4x - 7 = 0
Answer:
Part 1) The sum of the roots is [tex]4/3[/tex]
Part 2) The product of the roots is [tex]-7/3[/tex]
Step-by-step explanation:
Step 1
Find the roots
we have
[tex]3x^{2}-4x-7=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}-4x-7=0[/tex]
so
[tex]a=3\\b=-4\\c=-7[/tex]
substitute in the formula
[tex]x=\frac{-(-4)(+/-)\sqrt{-4^{2}-4(3)(-7)}} {2(3)}[/tex]
[tex]x=\frac{4(+/-)\sqrt{16^{2}+84}} {6}[/tex]
[tex]x=\frac{4(+/-)10} {6}[/tex]
[tex]x1=\frac{4+10} {6}=7/3[/tex]
[tex]x2=\frac{4-10} {6}=-1[/tex]
Step 2
Find the sum of the roots
[tex]x1+x2=(7/3)-1=4/3[/tex]
Step 3
Find the product of the roots
[tex]x1*x2=(7/3)*(-1)=-7/3[/tex]
A cab charges $1.50 for the first mile and $0.50 for each additional mile. Write and solve an inequality to determine how many miles Sharon can travel if she has $25 to spend.
A.$0.50 + $1.50x ≤ $25; x ≤ 16 miles
B.$0.50 + $1.50x ≥ $25; x ≥ 16 miles
C.$1.50 + $0.50x ≤ $25; x ≤ 47 miles
D.$1.50 + $0.50x ≥ $25; x ≥ 47miles
A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive if the apples are .99 per pound
Answer:
[tex]\$\,1.19[/tex]
Step-by-step explanation:
Quantity of apples bought by the student = 8.9 pounds
Amount paid by the student for apples bought by the student = [tex]\$[/tex] 10
If cost of one pound of apples is [tex]\$[/tex] 0.99 then cost of 8.9 pounds = 0.99 × Quantity of apples bought by the student = [tex]8.9\times 0.99=8.811[/tex]
Therefore,
Amount of change that the student receive if the apples are .99 per pound = Amount previously paid by the student for apples bought by the student when the student pays [tex]\$[/tex] 10 - Amount paid by the student for apples if the apples are .99 per pound = [tex]\$ \,10-\$ \,8.811=\$\,1.19[/tex]
An equilateral triangle has a semiperimeter of 6 meters. What is the area of the triangle? Round to the nearest square meter. 2 square meters 7 square meters 20 square meters 78 square meters
Select "Rational" or "Irrational" to classify each number.
Rational
Irrational
0.25
√0.25
√0.33
Answers
0.25 ⇒ It is rational
√0.25 ⇒ It is rational
√0.33 it is irrational
Explanation
a rational number is one that can be written as a ration. Or we can say that a rational number can be written as a/b where a and b are integers and b ≠0.
0.25 = 25/100
= 1/4
0.25 ⇒ It is rational.
√0.25 = 0.5
= 5/10
= 1/2
√0.25 ⇒ It is rational
√0.33 = 0.5744562664.......
This can not be written as a/b. So,√0.33 it is irrational
Final answer:
0.25 and √0.25 are rational numbers because they can be represented as ratios of integers, while √0.33 is an irrational number due to its inability to be precisely expressed as a fraction.
Explanation:
The question asks to classify each number (0.25, √0.25, √0.33) as either rational or irrational. The distinctions between rational and irrational numbers can be understood by recalling that rational numbers are those that can be expressed as a ratio of two integers, while irrational numbers cannot be exactly expressed as a fraction of two integers.
0.25: This can be expressed as the fraction 1/4, which is a ratio of two integers. Therefore, it is a rational number.
√0.25: The square root of 0.25 is 0.5, which can also be expressed as the fraction 1/2. Hence, this is also a rational number.
√0.33: This cannot be expressed as a precise fraction of two integers and its decimal representation is non-repeating and non-terminating. Therefore, it is an irrational number.
To classify, 0.25 and √0.25 are rational numbers because they can be represented as ratios of integers. √0.33 is considered an irrational number as it cannot be exactly expressed as a fraction.
If a man can run p miles in x minutes, how long will it take him to run q miles at the same rate?
It will take the man [tex]\( \frac{qx}{p} \)[/tex] minutes to run q miles at the same rate he runs p miles in x minutes.
Rate of running: The rate at which the man runs is given by the ratio of miles to minutes, which is [tex]\( \frac{p}{x} \)[/tex] miles per minute. This means he runs p miles in x minutes.Finding the time to run q miles: To find out how long it will take him to run q miles at the same rate, we use the formula:Time = [tex]\frac{\text{Distance}}{\text{Rate}}[/tex]
where Time is the time taken, Distance is the distance traveled, and Rate is the rate of running.
Substituting values: Substituting the given values, we have:Distance = q miles
Rate = [tex]\( \frac{p}{x} \)[/tex] miles per minute.
Therefore,
Time = [tex]\frac{q}{\frac{p}{x}}[/tex]
Simplify the expression: To simplify the expression, we can multiply the numerator and denominator by x to get rid of the fraction in the denominator:Time = [tex]\frac{qx}{p}[/tex]
The distance a body falls from rest varies directly as the square of the time the body is falling. If a body falls 81 ft. in 3 seconds, how far will it fall in 7 seconds?
witch set of numbers could represent the side lengths of a right triangle
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y=csc (x) - 9
a.
Vertical translation up 9 units
c.
Vertical stretch by a factor of 9
b.
Horizontal translation to the right 9 units
d.
Vertical translation down 9 units
Answer:
Option D is correct .i.e., Vertical translation down 9 units
Step-by-step explanation:
Given Function is y = cosec x - 9
Here basic function or parent function is y = cosec x
1. When constant ' a ' is added to to parent function or basic function then the function is translated vertically upward by a units.
2. When constant ' a ' is subtracted from parent function or basic function then the function is translated vertically downward by a units.
Therefore, Option D is correct .i.e., Vertical translation down 9 units
How do you solve the literal equation for g=6x solve for x
What is the completely factored form of f(x)=x3+5x2+4x−6?
f(x)=(x−3)(x−(−1+i3√))(x−(−1−i3√))
f(x)=(x+3)(x−(−1+i3√))(x−(−1−i3√))
f(x)=(x+3)(x−(−1+3√))(x−(−1−3√))
f(x)=(x−3)(x−(−1+3√))(x−(−1−3√))
The factored type is the product of constants and two-dimensional terms, that is the root of a function as well as the graph's x-intercepts, and the further calculation can be defined as follows:
Given:
[tex]\bold{f(x)=x^3+5x^2+4x-6}[/tex]
To find:
factored form=?
Solution:
[tex]\bold{f(x)=x^3+5x^2+4x-6}[/tex]
putting the value x=-1,-2,-3...... to find the function value 0.
[tex]\to \bold{f(-1)=-1^3+5(-1)^2+4(-1)-6}\\\\[/tex]
[tex]\bold{=-1+5\times 1+4 \times (-1)-6}\\\\ \bold{= -1+5-4-6} \\\\ \bold{=-6}\\\\[/tex]
[tex]\to \bold{f(-2)=-2^3+5(-2)^2+4(-2)-6}[/tex]
[tex]\bold{=-8+5\times 4+4 \times(- 2)-6}\\\\\bold{= -8+20-8-6}\\\\\bold{=-2}\\\\[/tex]
[tex]\to \bold{f(-3)=-3^3+5(-3)^2+4(-3)-6}[/tex]
[tex]\bold{=-27+5\times 9+4 \times(- 3)-6}\\\\\bold{= -27+45-12-6}\\\\\bold{=0}\\\\[/tex]
Therefore, [tex]\bold{(x+3)}[/tex] is the factor of the function.
Let [tex]\bold{(x+3)}[/tex] divide by the function:
[tex]\to \bold{\frac{x^3+5x^2+4x-6}{(x+3)}= x^2+2x-2}[/tex]
compare the value [tex]\bold{x^2+2x-2}[/tex] by the standard equation [tex]\bold{ax^2+bx+c=0}[/tex] so,
[tex]\bold{a=1}\\\\\bold{b=2}\\\\\bold{c=-2}\\\\[/tex]
Putting value into the quadratic equation formula:
[tex]\bold{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\bold{x=\frac{-(2) \pm \sqrt{(2)^2-4\times 1 \times -2}}{2\times 1}}\\\\\bold{x=\frac{-2 \pm \sqrt{4+8}}{2}}\\\\\bold{x=\frac{-2 \pm \sqrt{12}}{2}}\\\\\bold{x=\frac{-2 \pm 2\sqrt{3}}{2}}\\\\\bold{x=\frac{2(-1 \pm \sqrt{3})}{2}}\\\\\bold{x=(-1 \pm \sqrt{3})}\\\\\bold{x=(-1 + \sqrt{3}) (-1 -\sqrt{3})}\\\\[/tex]
Adding the factor value that is [tex]\bold{(x+3)}[/tex] so, the value is "[tex]\bold{(x+3)(-1+\sqrt{3})(-1-\sqrt{3}) }[/tex]"
So, the final answer is "[tex]\bold{f(x)=(x+3)(x-(-1+\sqrt{3}))(x-(-1-\sqrt{3}))}[/tex]"
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Spreadsheet software can be used to determine the amount of simple interest owed on a 30 day note. what mathematical operations would be used?
Final answer:
Spreadsheet software can be used to determine the amount of simple interest owed on a 30-day note by using the formula for simple interest: Principal (P) × Interest Rate (R) × Time (T).
Explanation:
In spreadsheet software, you can determine the amount of simple interest owed on a 30-day note using mathematical operations. The mathematical operations involved are multiplication and addition.
The formula for simple interest is:
Simple Interest = Principal (P) × Interest Rate (R) × Time (T)
For example, if you have a principal of $100, an interest rate of 5%, and a time period of 30 days, you can calculate the simple interest as:
$100 × 0.05 × (30/365) = $1.23
Therefore, the amount of simple interest owed on the 30-day note would be $1.23.
Torrid had $20 to but a birthday present for her dad. She decided to buy a DVD for $18. The sales tax is 7%. Does she have enough money? Explain your reasoning.
Please Show Work Too
Loren makes $9 per hr and Julie makes $12 per hour. What is the ratio between how much Loren makes per hour and how much Julie makes per hour?
Given random variable x is normally distributed, with a mean of 10 and standard deviation of 5, what is the probability that x is less than 11?
A stereo system cost $275. It was on sale for 15% off. The sales person receives a 2% commission. How much of a commission do they receive?
Answer:
They receive $4.68 as a commission
Step-by-step explanation:
The cost of stereo system = $275
Price after discount of 15% = 275 - (15% × 275)
= 275 - ( 0.15 × 275)
= 275 - 41.25
= $233.75
2% commission of the sales person = 2% × 233.75
= 0.02 × 233.75
= $4.675 ≈ $4.68
They receive $4.68 as a commission
how many lines of reflectional symmetry does an equilateral triangle have
Answer:
only 3 lines of symmetry does an equilateral triangle have.
Explanation:
Since a triangle can have 3 or 1 or no lines of symmetry.
In a equilateral triangle:
*All sides are equal
*All angles are equal i.e each of 60 degree.
Symmetry is when there is an exact replica or reflection of a shape or a line.
Line of symmetry: It is an imaginary line that runs through the center of a line or shape creating two perfectly identical halves.
A line of symmetry for a given triangle must go through each vertex as shown in figure;
Therefore, the equilateral with 3 sides equal has 3 lines of symmetry.
An equilateral triangle has [tex]\fbox{\begin\\\ 3\text{lines}\\\end{minispace}}[/tex] of reflection symmetry.
Further explanation:
A triangle is a two dimensional closed figure which is formed when three non-collinear points are joined. There are three sides, three angles and three vertices of a triangle.
On the basis of sides and angles triangles are classified as follows:
1) Scalene triangle: A triangle in which all the sides and the angles have a unique value is called a scalene triangle.
2) Isosceles triangle: A triangle in which any two sides or two angles are equal then the triangle is called an isosceles triangle.
3) Equilateral triangle: A triangle in which all the sides and the angles are equal then the triangle is called an equilateral triangle.
A line of reflection is defined as a line across which the image of a figure or an object is reflected.
The reflected image is of same size as of the original image.
In case of an equilateral triangle if we drop a median from one of the vertex of the triangle to its opposite side then it is observed that the median divides the equilateral triangle into two equal halves.
From figure 1 (attached in the end) it is observed that the median AD of an equilateral trinagle [tex]\triangle \text{ABC}[/tex] divides the triangle into two equal halves.
As per the above statement it is concluded that the median AD is the line of reflection symmetry for the equilateral triangle [tex]\triangle \text{ABC}[/tex].
Now, similarly if we drop a median form the vertex B or C to its opposite side then it is observed that the triangle into two equal halves.
Figure 2 (attached in the end) shows that the median dropped from the vertex B and C divides the triangle into two equal halves.
This implies that the median BD and CD are also the line of reflection symmetry for the equilateral triangle ABC.
So, the total number of lines of reflection symmetry for an equilateral triangle is [tex]3[/tex].
Thus, an equilateral triangle has [tex]3[/tex] lines of reflection symmetry.
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Answer details
Grade: High school
Subject: Mathematics
Chapter: Triangles
Keywords: Triangle, isosceles, scalene, equilateral, angles, vertex, non-collinear, reflection, symmetry, line of reflection, line of symmetry, median, reflected image.
The daily changes in the barometric pressure for four days are − − 0.05, 0.09, − − 0.04, and − − 0.08 inches. a. What is the mean change? Write your answer as a decimal. The mean change is inch. Question 2 b. The mean change after five days is − − 0.01 inch. What is the change on the fifth day? Write your answer as a decimal. The change on the fifth day is inch
of the 24 students in gregs class, 3/8 ride the bus to school. how many students ride the bus?
Answer:
9 students ride the bus.
Step-by-step explanation:
Given: The total number of students in gregs class is 24 and [tex]\frac{3}{8}[/tex] ride the bus to school.
To find how many students ride the bus;
Let x be the number of student ride the bus.
Proportional is simply a statement that the two ratios are equal.
It can be written in two ways i.e, [tex]\frac{a}{b} = \frac{c}{d}[/tex] or
[tex]a : b :: c :d[/tex]
Then, as per the given conditions;
x : 24 = 3 : 8 or
[tex]\frac{x}{24} = \frac{3}{8}[/tex]
Multiply both sides by 24 we get;
[tex]\frac{x}{24} \times 24 =\frac{3}{8} \times 24[/tex]
Simplify:
x = 9
Therefore, the student ride the bus is, 9
How to estimate 75x5?
To estimate 75 x 5 you first need to round 75 to 80 and then solve the multiplication.
How to estimate numbers?Estimating numbers implies rounding them if possible to simplify mathematical operations. Let's then round the numbers given:
75 = It can be rounded to 80, which is the nearest multiple of 10.
5 = It does not need to be rounded as this is already a simple number
Now after rounding each of the numbers involved, let's solve the mathematical operation, which in this case is multiplication.
80 x 5 = 400
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Identify two factors that have a product of 9/10.
what is the solution set of the equation x2 + 3x - 4 = 6
Find 8 x 397. Show your work and explain why the strategy you chose work best with factors.
HELP! I will give brainliest!
Felicity is placing a rectangle in the coordinate plane. She knows that the longer side of the rectangle is 3 times its shorter side. She places the longer side on the x-axis.
What coordinates should she assign to the top-right vertex of the rectangle?
Let
a-------> the shorter side of the rectangle
b------> the longer side of the rectangle
we know that
[tex]b=3a[/tex]
therefore
the dimensions of the rectangle are
[tex]3a*a[/tex]
the answer is
the coordinates of the top-right vertex are [tex](3a,a)[/tex]
What is the estimate of 1/2% of 412
How many $10 bills are the same as ten $1 bills
HELP!! what are the coordinates of the vertex of the parabola described by the equation below y=-5(x+2)^2+7
Answer: (-2,7)
Step-by-step explanation:
The circumference of a circular swimming pool is 100 feet. If the radius of the pool is doubled, what will the new circumference be?
Why am I wrong?
Picture attached.