Mathematics College

A pea seller had some peas. He sold 40% of his stock and still had 420 peas. Originally, he had how many peas?

Answers

Answer 1

100-40= 60%

60% = 0.60

420/0.60 = 700

he had 700 peas

Answer 2

420 --------60%
? ------------100%

100 x 420 / 60 = 700

answer
he had 700 peas originally

Related Questions

what is the equation to solve it

Answers

which equation has to be solved
Please ask your question

If (h, •) and (k, •) are subgroups of (g, •), prove that (h n k, •) is a subgroup of (g, •). can the same be said for the union, hu k? prove or give a counterexample.

Answers

Let [tex]\eta\in H\cap K[/tex]. Since both [tex]H[/tex] and [tex]K[/tex] are subgroups of [tex]G[/tex], we have

[tex]\eta\in H\cap K\implies\begin{cases}\eta\in H\\\eta\in K\end{cases}\implies\eta\in G[/tex]

Because both [tex]H,K[/tex] are subgroups of [tex]G[/tex], then [tex](H\cap K,\bullet)[/tex] contains the identity element [tex]e[/tex]. Furthermore, there must be some element [tex]\eta^{-1}\in H[/tex] and [tex]\eta^{-1}\in K[/tex], i.e. [tex]\eta^{-1}\in H\cap K[/tex], such that [tex]\eta\bullet\eta^{-1}=e[/tex].

Now let [tex]\eta_1,\eta_2,\eta_3\in H\cap K[/tex]. By the same reasoning as above it follows that each of these belong in [tex]G[/tex], and since [tex](G,\bullet)[/tex] is a group, we have [tex]\eta_1\bullet(\eta_2\bullet\eta_3)=(\eta_1\bullet\eta_2)\bullet\eta_3[/tex], so [tex]H\cap K[/tex] is associative under [tex]\bullet[/tex].

So [tex]H\cap K[/tex] contains the identity, is closed with respect to inverses, and is associative under [tex]\bullet[/tex]. Therefore [tex]H\cap K[/tex] must be a subgroup of [tex]G[/tex].

In the case of union, this is not always the case. Consider the group [tex](\mathbb Z,+)[/tex] with subgroups [tex](H,+)[/tex] and [tex](K,+)[/tex] where [tex]H[/tex] is the set of all integer multiples of 2 and [tex]K[/tex] is the set of all integer multiples of 3.

It's easy to show that [tex]H[/tex] and [tex]K[/tex] are indeed subgroups, but this is not the case for [tex]H\cup K[/tex]. We have

[tex]H\cup K=\{0,\pm2,\pm4,\ldots\}\cup\{0,\pm3,\pm6,\ldots\}[/tex]

Take the elements [tex]2\in H[/tex] and [tex]3\in K[/tex]. Addition yields [tex]2+3=5[/tex], but [tex]5\not\in H\cup K[/tex], so [tex]H\cup K[/tex] is not closed under [tex]+[/tex].

Given the Arithmetic sequence A1,A2,A3,A4A1,A2,A3,A4
29, 39, 49, 59

What is the value of A33A33?

Answers

The given sequence is
a₁ = 29
a₂ = 39
a₃ = 49
a₄ = 59

This sequence is an arithmetic sequence. Th first term is a₁ = 29, and the common difference is d= 10.

The n-th term is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
The 33-rd termis
a₃₃ = 29 + (33 - 1)*10
= 29 + 320
= 349

Answer: a₃₃ = 349

the oringinal cost of a lamp is $18.95. the lamp is on sale for 25% off. how much will you pay?

Answers

100% - 25% = 75%

so, if 18.95 is the 100%, how much is the 75% of that?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 18.95&100\\ x&75 \end{array}\implies \cfrac{18.95}{x}=\cfrac{100}{75}[/tex]

solve for "x".

It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
+ 5r = 8
+ 5r = 1
5() = r
= 5r

Answers

Let us say that the procedure of completely filling up the pool with water is called “1 job”. Therefore the rates of the equipment in doing the job would be:

Rate of handheld hose = 1 job / 8 minutes ---> 1

Rate of lawn sprinkler = r ---> 2

Rate of the two combines = 1 job/ 5 minutes ---> 3

So we are to find the equation to use, in this case, we simply have to add equations 1 and 2 to get 3:

1 / 8 + r = 1 / 5

Multiplying both sides by 5:

(5 / 8) + 5 r = 1 ---> ANSWER

Answer:

5/8 + 5r = 1

Step-by-step explanation:

Right on edge!

Problem Page
Lucy's shop sells
712
quarts of ice cream each day. How much is this in pints?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.

Answers

Because there are 2 pints in a quart, 712 quarts would equal 1,424 pints.

A given line has the equation 2x + 12y = −1.

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

Answers

2x + 12y = -1
12y = -2x - 1
y = - 1/6x - 1/12...slope here is -1/6. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular line will need a slope of 6.

y = mx + b
slope(m) = 6
(0,9)...x = 0 and y = 9
sub and find b, the y int
9 = 6(0) + b
9 = b

so ur perpendicular equation is : y = 6x + 9 <==

Answer

the answer is d

Step-by-step explanation:

A store has a $43.89 item on sale. The total discount of the sale is $9.66. What is the sale percentage off on this item?

Answers

well, if we take 43.89 to be the 100%, what is 9.66 off of it in percentage?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 43.89&100\\ 9.66&x \end{array}\implies \cfrac{43.89}{9.66}=\cfrac{100}{x}[/tex]

solve for "x".

A forest ranger can see for a distance of 12 miles from a firetower how many square miles can he observe?

Answers

using 3.14 for pi

area = pi x r^2

since he can see 12 miles in any direction 12 would be the radius

so 3.14 x 12^2 = 452.16 square miles

round the answer as needed.

why you delete my answer? it obviously was a legitamant answer.

How many degrees would the hour hand move in 4hrs?

Answers

a complete circle is 360 degrees, there are 12 numbers on a clock

360/12 = 30 degrees between each number

30 * 4 = 120 degrees in 4 hours

For an analysis of variance, the term “one-way” refers to

Answers

In statistics, you have statistical tests called ANOVA or Analysis of Variance. There is One-Way ANOVA and Two-Way ANOVA. You can only use One-Way ANOVA when you are testing only one dependent variable against at least two independent variables. For example, you want to find the statistics of the adsorption capacity with respect to two of its factors: pH and temperature. In this test, you only get the variance once and it is based on the F table of distibution. The other name for this, is actually the F-test.

Which of the following is not one of the three ways to express a ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4

Answers

3 of 4 is the wrong answer

3 of 4 is the incorrect way to express a ratio.

Whats the quotient of 2 1/4 and 5/8

Answers

[tex]\bf 2\frac{1}{4}\implies \cfrac{2\cdot 4+1}{4}\implies \cfrac{9}{4}\\\\ -------------------------------\\\\ \cfrac{9}{4}\div \cfrac{5}{8}\implies \cfrac{9}{4}\cdot \cfrac{8}{5}\implies \cfrac{9\cdot 8}{4\cdot 5}\implies \cfrac{72}{20}\implies \cfrac{18}{5}\implies 3\frac{3}{5}[/tex]

A flat rectangular piece of aluminum has a perimeter of 66 inches. The length is 15 inches longer than the width. Find the width.

Answers

x is the length
y is the width
2x+2y=66
x-y=15
multiply the second equation by 2 (elimination)
2x-2y=30
add the equations together
4x=96
x=24
Plug this in to one of the original equations
24-y=15
the width is 9

The infinite sequence –1, –2, –3, –4, –5, ... can be generated with which explicit formula?

Answers

Answer:

An = (-1)* n

Step-by-step explanation:

An = ( -1) * n

A2 = (-1 ) * 2 = -2

A3= ( -1 ) * 3 = -3

A4= ( -1 ) * 4 = -4

A5= ( -1 ) * 5 = -5

An explicit formula also known as an exact formula is a mathematical formula used to find the nth term in a series or sequence . hence the explicit formula used to find the nth term of this sequence can be represented as

An = ( -1 ) * n where n = number of the next term

Answer:

Step-by-step explanation:

i got it right

One bag of Glizard wood chips covers a 215 square foot area. How many total bags of wood chips must be purchased to cover an area that is 42 feet by 61 feet?

Answers

42 x 61 = 2562

2562/215 = 11.92

12 total bags are needed

For what values of b will f(x)= log b^x be an increasing function?

Answers

[tex]log(b^x) = xlog(b)[/tex]

This is basically a line with slope [tex]log(b)[/tex]

For this to be an increasing function, the slope has to be greater than 0.

[tex]log(b) \ \textgreater \ 0\\ b \ \textgreater \ 10^0\\ b \ \textgreater \ 1[/tex]

So f(x) will be an increasing function for all b > 1

Using logarithmic function concepts, it is found that for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.

What is an logarithmic function?

A logarithmic function is modeled by:

[tex]f(x) = \log_b{x}[/tex]

The coefficient b determines the behavior of the function, as follows:

b > 1: The function is increasing.b < 1: The function is decreasing.

Hence, for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.

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Davis Construction is building a new housing development. They begin by mapping the development out on a coordinate grid. They place one of the two swimming pools at (-4, -1) and another at (6, 3). If they want the clubhouse to be exactly halfway between the two pools, find the coordinates of the clubhouse.

Answers

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -4}}\quad ,&{{ -1}})\quad % (c,d) &({{ 6}}\quad ,&{{ 3}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{{{ 6}} -4}{2}\quad ,\quad \cfrac{3-1}{2} \right)[/tex]

Paula has 3 bananas. She wants to divide each of them into sections. How many 's are there in 3 bananas?

Answers

Answer:

B IS 21

Step-by-step explanation:

Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x4 + 5 / x5 + 2x3

Answers

[tex]\dfrac{x^4+5}{x^5+2x^3}=\dfrac{x^4+5}{x^3(x^2+2)}=\dfrac ax+\dfrac b{x^2}+\dfrac c{x^3}+\dfrac{dx+e}{x^2+2}[/tex]

Ohm’s Law states that the electrical current, I in amperes, through a resistor is given by the formula 644-14-04-00-00_files/i0210000.jpg where V is the voltage in volts and R is the resistance in ohms. If the current is 6 amperes and the resistance is 18 ohms, what is the voltage?

Answers

if im am correct its V=I * R sooo 108 = 6 * 18

Your Answer is 108 volts

Answer:

The correct answer is D., or "108 volts".

A set of data with a mean of 62 and a standard deviation of 5.7 is normally distributed. what is the value that is −1 standard deviation from the mean

Answers

Here, the mean is 62 and the std. dev. is 5.7 One standard dev below the mean is thus calculated as 62 - 5.7, or 56.3. This is equivalent to "the mean less one std. dev.")

A kitchen assistant knocked over a cooling rack and spilled 12% of the cookies onto the floor Francesca had
to bake 36 more cookies to replace them.
how many cookies were ordered in total

Answers

300 cookies because 36/.12=300.

Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5

Answers

2(x + 1) - (-x + 5) < = -18
2x + 2 + x - 5 < = -18
3x - 3 < = -18
3x < = -18 + 3
3x < = -15
x < = -15/3
x < = - 5 <==

Answer:

Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5

Step-by-step explanation:

2 (x + 1) - (-x + 5) ≤ -18

2x + 2 + x - 5 ≤ - 18

3x - 3 ≤ - 18

3x ≤ - 15

x ≤ - 15/3 ≤ - 5

The answer is: D. x ≤ - 5

A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed

Answers

Your question asks for an expression, so you would expect an answer in the form of an equation containing variables. This is because you have only 2 independent equations with 3 unknowns. That makes the system unsolvable.

Suppose v₁ is the mountaineer's velocity during the 1,000-foot trail. Then, v₂ is his speed for the 5,000-foot trail. The equation relating these two variables is:

v₂ = 2v₁ - 10 ---> equation 1

Then, you find the equation for the total number of hours he climbed. That would be the distance divided by their respective speed.

t = 1000/v₁ + 5000/v₂ ----> equation 2

Substituting equation 1 to equation 2,

t = 1000/v₁ + 5000/(2v₁ - 10)
t = 1000/v₁ + 5000/2(v₁-5)
t = 1,000/v₁ + 2,500/(v₁-5)

The equation that represents the number of hours the mountaineer climbed is t = 1000/V1 + 2600(V1 - 5).

How to compute the equation?

Based on the information given, V1 = 1000 and V2 = 2V1 - 10.

The time taken will be:

= 1000/V1 + 5000/V2

Well substitute the equations. This will be:

t = 1000/V1 + 5000//(2V1 - 10)

t = 1000/V1 + 5000/2(V1 - 5)

t = 1000/V1 + 2600(V1 - 5).

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Is 703.005 is greater than or less than seven hundred three and five hundredths

Answers

703.005 is less because .005 is less than .050

John has taken out a loan for college. He started paying off the loan with the first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he payed the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of the first 20 payments using complete sentences.

Answers

John's payments are
month 1: $100
month 2: $100*(1.1)
month 3: $100*(1.1)²
month 4: $100*(1.1)³

...

The payments form the geometric sequence
a, ar, ar², ..., arⁿ
where
a = $100
r = 1.1

The sum of the first n terms is
[tex]S_{n} = \frac{a(1-r^{n})}{1-r} [/tex]

Therefore the sum of the first 20 payments is
S₂₀ = [$100(1 - 1.1²⁰)]/(1 - 1.1)
= $5727.50

John makes a total of $5727.50 in the first 20 payments.

In a certain town 22 of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure

Answers

What is the equation.

Answer:

4.6

Step-by-step explanation:

Allow me to revise your question and hope it will be the same as the original one:

In a certain town 22% of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure

a. 1.9

b. 13

c. 4.6

d. 3.6

Here is my answer:

Given:

22% of voters favor a given ballot = 0.22 Groups of 21 voters

So the variance is: 21*0.22 = 4.6

We choose B

Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 4, 8, 32 3 .

Answers

Let [tex]x=t[/tex], so that

[tex]x^2=2y\implies t^2=2y\implies y=\dfrac{t^2}2[/tex]

[tex]3z=xy\implies3z=\dfrac{t^3}2\impiles z=\dfrac{t^3}6[/tex]

Then the length of the path is

[tex]\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2+\left(\frac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^4\sqrt{1+t^2+\frac{t^4}4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4\sqrt{4+4t^2+t^4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4\sqrt{(t^2+2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4(t^2+2)\,\mathrm dt[/tex]
[tex]=\dfrac{44}3[/tex]

Final answer:

To find the exact length of the curve c from the origin to a given point, we can parameterize the curve and use the formula for arc length. In this case, we need to solve for x, y, and z in terms of a parameter t. Then, we can integrate the arc length formula to obtain the exact length.

Explanation:

To find the exact length of the curve c from the origin to the point (4, 8, 32/3), we need to first parameterize the curve. Given that x2 = 2y and 3z = xy, we can solve for x, y, and z in terms of a parameter t. Then, we can use the formula for arc length to calculate the length of the curve using integration.

Let's begin by solving for x, y, and z in terms of t:

From x2 = 2y, we have x = √(2t) and y = t2/2.Substituting these values into 3z = xy, we get 3z = √(2t) * (t2/2) or z = (t3√2)/6.

Now, we can calculate the arc length using the formula:

L = ∫ sqrt((dx/dt)2 + (dy/dt)2 + (dz/dt)2) dt

Plugging in the values of x, y, and z in terms of t, we can evaluate the integral to find the exact length of curve c.

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Use a triple integral to find the volume of the given solid. the solid enclosed by the cylinder x2 + y2 = 9 and the planes y + z = 14 and z = 2.

Answers

Using cylindrical coordinates, we have

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}[/tex]

so that the Jacobian gives

[tex]\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta[/tex]

The volume is given by the triple integral

[tex]\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\int_{\zeta=2}^{\zeta=14-r\sin\theta}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}r(14-r\sin\theta-2)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}(12r-r^2\sin\theta)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_{\theta=0}^{\theta=2\pi}(54-9\sin\theta)\,\mathrm d\theta[/tex]
[tex]=108\pi[/tex]

Final answer:

To find the volume of the solid enclosed by the given cylinder and planes, you convert to cylindrical coordinates. Then, you set up a triple integral with respect to these coordinates as ∫∫∫ dz dr dθ where the bounds of integration are 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.

Explanation:

The volume of the solid can be found using a triple integral in cylindrical coordinates. First, we need to identify the boundaries of the solid. From the cylinder equation, we see that x² + y² = 9, which in cylindrical coordinates converts to r^2 = 9, so 0<=r<=3. Then, from the plane equations y + z = 14 and z=2, we can determine that in cylindrical coordinates, 2<=z<=14-r.

Therefore, the volume V can be found by:

V = ∫∫∫ dz dr dθ

with bounds for integration being 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.

Running this triple integral will provide the volume of the solid.

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