Pamela is 1 year old now.
How to solve problems on ages ?
If the present age of a person be X, thenAge after n years = X +n
Age n years ago = X - n
n times the present age = nX
If ages in the numerical are mentioned in the ratio A : B, then A : B will be AX and BX.
If the sum of ages is X and Y and the ratio of their ages is p : q respectively, then you can determine the age of Y by using the formula shown below:Age of Y = Ratio of Y / Sum of ratios x sum of ages
Age of Y = q/ (p +q) x A
In the given statement is:
Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra.
To find the how old is Pamela now.
Now, Based on the given conditions,
Formulate:
Let x be the Pamela's age
6 + 7 + x = 2(6 + x)
13 + x = 12 + 2x
x - 2x = 12 - 13
-x = -1
x = 1
Hence, Pamela is 1 year old now.
Learn more about Age at:
https://brainly.com/question/11805078
#SPJ1
The revenue function for a real estate agency is based on a percentage of the amount of monthly sales made by agents. The cost function for the agency is based on the commissions, paid to the agent plus the fixed monthly costs. both functions are shown below where X is the dollar amount of the monthly sales made by agents.
• Revenue function: f (x) = 0.03
• Cost function: g (x) = 0.015x + 4,600
The agency will break, even when the revenue function is equal to the cost function. For the agency to break even, what amount of monthly transactions, in dollars, must be generated by its agents?
• Between $0 and $2000
• Between $4,500 and $4,700
• Between $153,000 and $155,000
• Between $305,000 and $307,000
Answer:
D. Between $305,000 and $307,000
Step-by-step explanation:
A. This is a result of finding 4,600(0.03 + 0.015).
B. This is a result of using the y-intercept for the cost function.
C. This is a result of incorrectly solving the equation 0.03x = 0.015x + 4,600 by dividing 4,600 by 0.03
instead of 0.015 in the final step.
D. This is a result of correctly solving the equation 0.03x = 0.015x + 4,600 ⇒ 0.015x = 4,600 then dividing
4,600 by 0.015 to get approximately 306,667.
1. An oil tank has a circular cross section of radius 2.1 metres. It is filled to a depth of 3.4 metres. a) Calculate x, the width in metres of the oil surface. 3-4 m b) What other depth of oil would give the same surface width? 2.1m
Answer:
Step-by-step explanation:
A) We can find half of the width of the surface by applying pythagorean theorem on the right angled triangle formed by three points which are the center of the circle, the point on the circle where the the endpoints of the width and the radius meet, and the midpoint of the width.
let radius=r, width=w
[tex]r^2=(w/2)^2+(3.4-2.1)^2\\[/tex], since the distance between the origin and the midpoint of the width is 3.4m-2.1m.
[tex]-(w/2)^2=(3.4-2.1)^2-r^2, r=2.1\\-(w/2)^2=(1.3)^2-(2.1)^2\\-(w/2)^2=1.69-4.41\\-(w/2)^2=-2.72\\w/2=\sqrt{2.72}\\w=2*\sqrt{2.72}\\w=3.3 meter[/tex]
B) we can find the other depth of oil which can give the same surface area of oil if the now empty part of the cylinder is filled with oil and the now filled part of the cylinder is empty, so the other possible depth for the same surface area of oil is the diameter of the circle minus 3.4 meters:
diameter=4.2 meter, 4.2 meter-3.4 meter:
0.8 meter depth
a. The width (x) of the oil surface is approximately 5.348 meters.
b. Another depth of oil that would give the same surface width (x ≈ 5.348 meters) is approximately 3.402417 meters.
a) Here, we have to calculate the width (x) of the oil surface, we need to find the length of the chord of the circular cross-section at the top of the oil tank.
We can use the formula for the length of a chord in a circle when the depth and radius are known.
Given that the radius (r) of the circular cross-section is 2.1 meters and the depth (d) of the oil is 3.4 meters, the width (x) can be calculated as follows:
x = 2 * √(r * d)
x = 2 * √(2.1 * 3.4)
x = 2 * √(7.14)
x ≈ 2 * 2.674
x ≈ 5.348 meters
So, the width (x) of the oil surface is approximately 5.348 meters.
b) Now, let's find the other depth of oil that would give the same surface width (x = 5.348 meters).
We can rearrange the formula to solve for the depth (d):
x = 2 * √(r * d)
Divide both sides by 2:
x/2 = √(r * d)
Square both sides:
(x/2)² = r * d
Now, plug in the given values (x = 5.348 meters and r = 2.1 meters) and solve for d:
(5.348/2)² = 2.1 * d
2.674² = 2.1 * d
7.145076 = 2.1 * d
Divide by 2.1:
d ≈ 7.145076 / 2.1
d ≈ 3.402417
So, another depth of oil that would give the same surface width (x ≈ 5.348 meters) is approximately 3.402417 meters.
Learn more about circle here:
brainly.com/question/11833983
#SPJ7
Evaluate each expression if x is 2/5, y is -4, and z is -0.2. Then match each expression with the correct answer.
A) 1x + y + z
B) 1 x + y + z
C) 2(y)(x)
D) 2 (y)(x)
E) 32x - z
F) 3 2x - z
G) 4x + y
The expressions evaluated for the given values of x, y, and z, and matched to the values are
1x + y + z → -3.8
2(y)(x) → -3.2
32x - z → 13
4x + y → -2.4
Evaluating an expressionFrom the question, we are to evaluate the given expressions for the given values of x, y and z
The given values of x, y, and z are
x = 2/5, y = -4, and z = -0.2
A. 1x + y + z
1(2/5) + (-4) + (-0.2)
2/5 - 4 - 0.2
0.4 - 4 - 0.2
= -3.8
C) 2(y)(x)
2(-4)(2/5)
-8(0.4)
= -3.2
E) 32x - z
32(2/5) - (-0.2)
32(0.4) + 0.2
12.8 + 0.2
= 13
G) 4x + y
4(2/5) + (-4)
4(0.4) - 4
1.6 - 4
= -2.4
Hence, the expressions evaluated for the given values of x, y, and z, and matched to the values are
1x + y + z → -3.8
2(y)(x) → -3.2
32x - z → 13
4x + y → -2.4
Learn more on Evaluating an expression here: https://brainly.com/question/23133222
#SPJ1
Solve w^2=36 where is a real number. Simplify your answer as much as possible.
Answer:
w = 6 (or) w = -6
Step-by-step explanation:
Let's solve the problem,
→ w² = 36
→ w = √36
→ w = + 6
→ w = 6 (or) w = -6
Thus, the answer is 6 & -6.
The cost of 4 tables and 3 chairs is $695. If the table costs $25 more than the chair, find the cost of a
table.
Answer:
110 bucks
Step-by-step explanation:
4t+3c=695
c=t-25
4t+3(t-25)=695
7t=770
t=110
4 is a rational number because it can be written as the fraction 4/1. True of false?
Answer:
true
Step-by-step explanation:
1 + 1 please also explain as much as possible
Answer: 2
Step-by-step explanation:
Please open this:
transistors are used to build computer chips. The size of the earliest transistors
The number of times that the old transistor is bigger than the new ones in the computer is 1 × 10^6.
How to illustrate the information?It should be noted that the the side of the earliest form of transistors for computer was 1 × 10⁴.
Now, the size of the transistor today was illustrated as 1 × 10^-².
Therefore, the difference in size will be about:
= 1 × 10⁴ / 1 × 10^-²
= 1 × 10^6
Therefore, the number of times that the old transistor is bigger than the new ones in the computer is 1 × 10^6.
Learn more about computers on:
brainly.com/question/24540334
#SPJ1
Please please please please please please please please please help me I don’t know this question asking questions like this like I’m in high school
Answer:
Multiplication -- > 6 × 3 - 8
Division --> (4 + 3)/2
Subtraction --> 4 - 5 + 7
Addition --> 15 + 8 ÷ 4 - 6
Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay. Describe a real-world situation in which opposite quantities combine to make zero.
A real-world situation in which opposite quantities combine to make zero is that "John bought 4 oranges and gave his friend 4 oranges. How many does he have?
How to illustrate the information?It should be noted that the information is that we should real-world situation in which opposite quantities combine to make zero.
An example will be that John bought 4 oranges and gave his friend 4 oranges.
The number of oranges that he has left will be:
= 4 - 4
= 0
Therefore, the combination gives zero.
Learn more about essays on:
brainly.com/question/25607827
#SPJ1
Use what you know about scientific notation to write the number -20,000 with a power of 10.
- 20,000
- 20,000=
(Type your answer in scientific notation using the appropriate symbol from the math palette for any multiplication.)
Help me solve this View an example Get more help.
Review Progress
+
x
#
More
Question
The scientific notation to write the number -20,000 with a power of 10.
The scientific notation to write the number -20,000 with a power of 10 is -2 ×10⁴.
Given that
The number is -20,000To find
We have to find the scientific notation form of number -20,000So, according to the question
We have
The number = -20,000For finding the scientific notation form of given number, first we have to know about scientific notation with a power of 10.
Scientific notation with a power of 10
To write any number with the help of power of 10 in very easy way is telling Scientific notation with a power of 10 . Because in that universe there is a lots of smallest and largest number present, so we can't write every numbers in single page. To write that numbers in very easy way the scientists was create a way to write that numbers with the help of power of 10.
So, now we can convert that number in a form of Scientific notation.
n = -20,000
Now multiply [tex]\frac{10^4}{10^{4}}[/tex], we will get
n = -20,000 × [tex]\frac{10^4}{10^{4}}[/tex]
n = [tex]\frac{-20,000\times 10^4}{10000}[/tex]
n = - 2× 10⁴
The scientific notation with the power of 10 form of -20,000 is - 2× 10⁴.
To learn more about scientific notation , please click on the link:
https://brainly.com/question/10458842
#SPJ9
Let [tex] \rm\hat{i}, \hat{j} \: and \: \hat{k} [/tex] be the unit vector along the three positive coordinate axes. Let [tex] \rm\overset{ \to}a = 3 \hat{i} + \hat{j} - \hat{k} ,\\ \rm \overset{ \to}b = \hat{i} + b_{2} \hat{j} + b_3\hat{k}, \: \: \: \: \: \: \: b_{2}, b_{3} \in \mathbb{R}, \\ \rm\overset{ \to}c= c_{1} \hat{i} + c_{2} \hat{j} + c_3\hat{k}, \: \: \: \: \:c_{1},c_{2}, c_{3} \in \mathbb{R}[/tex]
be three vectors such that [tex] \rm b_2b_3 > 0, \overset{ \to}a \cdot\overset{ \to}b = 0[/tex] and [tex] \left(\begin{gathered} 0& \rm - c_{3} & \rm c_{2} \\ \rm c_{3}& \rm 0 & \rm - c_{1} \\ \rm - c_{2}& \rm c_{1} & \rm 0 \end{gathered} \right) \left(\begin{gathered} 1 \\ \rm b_{2} \\ \rm b_3\end{gathered} \right) = \left(\begin{gathered} \rm3 - c_{1} \\ \rm 1 - c_{2} \\ \rm - 1 - c_3\end{gathered} \right)[/tex]
Then which of the following is true
[tex] \rm(1) \: \overset{ \to}a \cdot\overset{ \to}c = 0 \\ \rm(2) \: \overset{ \to}b \cdot\overset{ \to}c = 0 \\ (3) \: \overset{ \to}{| \rm b|} > \sqrt{10} \\(4) \: \overset{ \to}{| \rm c|} \leq \sqrt{11}[/tex]
Computing the matrix product in the last condition gives a system of linear equations in the components of [tex]\vec c[/tex],
[tex]\begin{cases} c_1 + b_3c_2 - b_2c_3 = 3 \\ -b_3c_1 + c_2 + c_3 = 1 \\ b_2c_1 - c_2 + c_3 = -1 \end{cases}[/tex]
and is easily solvable to get
[tex]c_1 = \dfrac{6-2b_3}{2+{b_2}^2+{b_3}^2}, c_2 = \dfrac{2+3b_3}{2+{b_2}^2+{b_3}^2}, c_3 = \dfrac{9-3b_3}{2+{b_2}^2+{b_3}^2}[/tex]
or, using the condition [tex]\vec a\cdot\vec b = 3 + b_2 - b_3 = 0[/tex],
[tex]c_1 = -\dfrac{2b_2}{11 + 6b_2 + 2{b_2}^2}, c_2 = \dfrac{11+3b_2}{11+6b_2+2{b_2}^2}, c_3 = -\dfrac{3b_2}{11+6b_2+2{b_2}^2}[/tex]
• (1) is false, since
[tex]\vec a \cdot \vec c = \dfrac{11}{2 + {b_2}^2 + {b_3}^2} \neq 0[/tex]
because [tex]{b_2}^2+{b_3}^2\ge0 \implies 0<\vec a\cdot\vec c\le\frac{11}2[/tex].
• (2) is true.
[tex]\vec b\cdot \vec c = \dfrac{(3 + b_2 - b_3) (2 + 3b_3)}{2 + {b_2}^2 + {b_3}^2} = \dfrac{(\vec a\cdot\vec b)(2+3b_3)}{2+{b_2}^2+{b_3}^2} = 0[/tex]
• (3) is false. The magnitude of [tex]\vec b[/tex] could be smaller than √10.
Since [tex]\vec a\cdot\vec b=0[/tex], we have
[tex]\|\vec b\| = \sqrt{1 + {b_2}^2 + (3+b_2)^2} = \sqrt{10 + 6b_2 + 2{b_2}^2}[/tex]
and
[tex]2{b_2}^2 + 6b_2 = 2\left({b_2}^2 + 3b_2 + \dfrac94\right) - \dfrac{18}4 = 2\left(b_2 + \dfrac32\right)^2 - \dfrac92 \ge - \dfrac92[/tex]
which is to say, [tex]\|\vec b\| \ge \sqrt{10-\frac92} = \sqrt{\frac{11}2}[/tex].
• (4) is true.
We have
[tex]\|\vec c\| = \dfrac{\sqrt{11} \sqrt{11 - 6b_3 + 2{b_3}^2}}{2 + {b_2}^2 + {b_3}^2}[/tex]
In terms of [tex]b_2[/tex] alone,
[tex]\|\vec c\| = \dfrac{\sqrt{11}\sqrt{11 + 6b_2 + 2{b_2}^2}}{11+6b_2+2{b_2}^2} = \dfrac{\sqrt{11}}{\sqrt{11+6b_2+2{b_2}^2}}[/tex]
Now,
[tex]11 + 6b_2 + 2{b_2}^2 = 2\left(b_2+\dfrac32\right)^2 + \dfrac{13}2 \ge \dfrac{13}2[/tex]
which means
[tex]\|\vec c\| \le \dfrac{\sqrt{11}}{\sqrt{11 + \frac{13}2}} \le \sqrt{11}[/tex]
HELPPPPPPPP!!!!! 50 POINTS!
Answer:
a, b, a/2, b/2
Step-by-step explanation:
The coordinates of C are (a,b).
You find the midpoint by taking the averages of the coordinates.
The third blank is a/2.
The fourth blank is b/2.
Answer:
a, b, a/2, b/2
Step-by-step explanation:
Solve: 3⁴ × 3² × 3³
...............................
Answer:
19,683
Step-by-step explanation:
3⁴ × 3² × 3³
Solve the exponents
81 x 9 x 27
Multiply each number and you get
19,683
ASAP not that hard for 15 points
Answer:
24
Step-by-step explanation:
When 2 gallons of gasoline is added the tank goes from 1/6 full to 1/4 full. So the equation is:
2 = (1/4 - 1/6)x
2 = (1/12)x
x = 24
Total capacity of the tank is 24 gallons.
I watched ad still does not let me see answer!
Answer:
That's unfortunate. :(
Sohan and his sister ate 2/5 of 25 chocolates. How many chocolates they didn't eat?
Sin^-1(x) when x=0.3
Solve by using limits (h—>0)
Answer:
please rate as brainliest
In which interval is the radical function f of x is equal to the square root of the quantity x squared 2 times x minus 24 end quantity increasing?
We get that the function f (x) = √ x² - 2 x - 24 is increasing at the interval [6, ∞).
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
We are given the function as:
f (x) = √ x² - 2 x - 24
From the graph, the function f (x) = √ x² - 2 x - 24 is increasing over the interval [6, ∞).
Therefore, we get that the function f (x) = √ x² - 2 x - 24 is increasing at the interval [6, ∞).
Learn more about function here:
https://brainly.com/question/4025726
#SPJ9
K
Order the numbers below from least to greatest.
1
2-3√6, -7,34
Choose the correct answer below.
O A.
2₁
7
OB. 7
O C. -3,
OD. -3,
7
4'
-
3.4, √6,-3
3.4, √6
7 1
42 √6,3.4
7 1
42.3.4, √6
Answer:
the anwser is B
Step-by-step explanation:
B is the best option choice given
Answer:
1. -7, -3, square root of 6, 2, 34
Step-by-step explanation:
Solve these absolute value equations.
18. |3р + 7| = 6p
The absolute value of the given statement is a -3/7 and 3/7.
According to the statement
We have to find that the value of the absolute equations.
So, For this purpose, we know that the
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
From the given information:
|3р + 7| = 6p
And we know that the
If we want to solve equations with absolute values we must know we have to find the solution for both positive and negative values. This is because positive and negative values have a positive absolute value.
Then
|3р + 7| = 6p
6p - 3p = 7
3p = 7
Then
p = 3/7.
According to the absolute value the answer become -3/7 and 3/7.
So, The absolute value of the given statement is a -3/7 and 3/7.
Learn more about absolute value function here
https://brainly.com/question/3381225
#SPJ9
Describe the continuity of the graphed function.
A. The function is continuous.
B. The function has a removable discontinuity at x=0.
C. The function has a jump discontinuity at x=0.
D. The function has an infinite discontinuity at x=0.
The correct option regarding the continuity of the function at x = 0 is given by:
A. The function is continuous.
What is the missing information?
The graph is missing, and is given at the end of this problem.
A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
From the graph of the function, at x = 0, we have that:
[tex]\lim_{x \rightarrow 0^-} f(x) = \lim_{x \rightarrow 0^+} f(x) = f(0) = 0[/tex]
Which means that the function is continuous at x = 0, hence option A is correct.
More can be learned about continuity of a function at https://brainly.com/question/24637240
#SPJ1
A quadratic function is shown on the graph.
a downward opening parabola beginning with open circle at negative 3 comma negative 7 increasing to a vertex at 0 comma 2 and then decreasing to a closed circle at 2 comma negative 2
What is the range of the function?
{y | −7 < y ≤ 2}
{y | −7 ≤ y ≤ 2}
{x | −3 ≤ x ≤ 2}
{x | −3 < x ≤ 2}
The range of the quadratic function is shown on the graph.is {x | −3 ≤ x ≤ 2}
What is a quadratic function ?
A quadratic function is a type of function that has polynomials, if the polynomial in a quadratic function is of degree two then the polynomial is said to be quadratic. we can therefore say that quadratic functions are a special type of polynomials with a power of 2
The graph of a quadratic function is represented by a curve opening upward or downward, it may also open sideways depending on ow the values are chosen.
The range are the input values, they are on the x axis. Form the description of the graph the range is fount to be {x | −3 ≤ x ≤ 2}
Read more on quadratic functions here: https://brainly.com/question/1214333
#SPJ1
True or false: An equation in the form of A x + B y = C , where A ≥ 0 , A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1 can represent either a linear or nonlinear function.
Answer:
True
Step-by-step explanation:
This will always be the equation of a line, which represents a linear function.
Use compatible numbers to estimate the whole number quotients 5320/61?
The whole number quotients of the expression; 5320/61 as required to be evaluated in the task content is; 88.
What is the best estimate of the whole number quotients of the expression; 5320/61 as given in the task content?It follows from the task content that the use of compatible numbers is to be used to estimate the whole number quotients 5320/61.
On this note, since the numbers can be written as follows;
= (53.2 × 100)/(0.61 × 100)
= 53.2/0.61
The estimate can therefore be determined by evaluating;
= 53/0.6
= 88 remainder 1.
Therefore, the closest estimate of the whole number quotients 5320/61 as given in the task content is; 88.
Ultimately, the whole number quotients of the expression; 5320/61 as required to be evaluated in the task content is; 88.
Read more on quotients;
https://brainly.com/question/16720439
#SPJ1
Tn=2[n-1]-5 find t14
habbsbzbzbzbzbbzbBbbababsbsbsbsbsbs
URGENT!!⚠️
a local record store invested $400,000 in charitable trust fund so that they can offer scholarships to their employees. the interest rate is 4.2% compounded quarterly. how much interest is available from the trust fund for the scholarships each year?
Answer:
I am here to help!
Step-by-step explanation:
if it's each year won't the company have 168k?
If sin theta= 1/4 and theta is acute, find tan
(pi/2- theta).
Answer:
3.8723
Step-by-step explanation:
[tex]sin(\theta) = \frac{1}{4}[/tex]
So [tex]\theta = sin^{-1}(\frac{1}{4}) = 0.25268[/tex] radians or [tex]14.48^{\circ \:}[/tex]
[tex]\frac{\pi}{2}} \text\;in\;radians=90 ^{\circ}[/tex]
[tex]\text{So\;} \frac{\pi}{2} - \theta = 90 - 14.48 = 75.52^{\circ}[/tex]
[tex]\tan(\frac{\pi}{2}-\theta) = \tan(75.52) = 3.8723[/tex]
9x{[14÷2+(4‐1)]-8 can someone show step by step?
Answer:
82
Step-by-step explanation:
9 x {[14÷2+(4‐1)] - 8
9 x {[7 + (3)] - 8
9 x [7 + 3] - 8
9 x [10] - 8
90 - 8
82
I hope this helps!
Write the following number in decimal notation.
Four hundred twenty-seven thousandths
Writing Four hundred twenty-seven thousandths in decimal notations gives 0.0000023419
How to write Four hundred twenty-seven thousandths in decimal notationGiven data
Four hundred twenty-seven thousandths
Four hundred twenty-seven thousand is written in figures as follows
400 000 + 20 000 + 7 000 = 427000
Four hundred twenty-seven thousandths = 1 / 427000
using calculator gives
= 2.3419 * 10^-6 ( in standard form )
= 0.0000023419 ( in decimal notation)
what is decimal notations?This a term in mathematics used to refer to a way of rewriting numbers in fractions to decimal form. it consists of a value and a point, then the required numbers.
The point is called decimal point. Decimal notations is not used only for numbers less than one. So are numbers in fractions, numbers in decimal may be greater than one. However the question refers to number that is less than one.
The given number: Four hundred twenty-seven thousandth is written in fraction as: 1 / 427000
then from fraction we write the decimal notation using calculator or long division to get 0.0000023419.
Read more on decimal notations here: https://brainly.com/question/795817
#SPJ1