Answer:
15 baskets
Step-by-step explanation:
A 120-gallons (gal)tank initially contains 90 lb of a salt dissolved in 90 gal of water. Brine containing 2 lb/gal of salt flows into the tank at the rate of 4gal/min. The mixture is kept uniform by stirring, and the stirred mixture flows out at the rate of 3gal/min. How much salt does the tank contain when it is full
Answer:
The tank will contain 202 Ib of salt when it's full.
Step-by-step explanation
To find the amount of salt in the tank at time t= x(t)
If x(0)= 90Ib
To find the volume of the tank at time t
V(t)= 90+(4-3)t=90+t gal
Other solutions are found attached
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
Consider the following numbers Which of these numbers are counting numbers?
{9 ,1, 4/5, √16 , 0.7 , -1, -√2 , π , 0}
The counting number(s) is/are _______(Use a comma to separate answers as needed Do not simplify.)
Answer:
9, 1
Step-by-step explanation:
Counting numbers are numbers that can be used for counting purposes. This group of numbers does not include negative numbers, fractions, zero, decimal numbers etc. They are positively directed whole numbers.
From the question, given the condition not to simplify, then the counting numbers are:
9, 1
others numbers can not be referred to as counting numbers.
x/x-2+x-1/x+1=-1
I'm having trouble figuring this out, an explanation on how to solve would suffice.
Answer:
x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Step-by-step explanation:
Solve for x over the real numbers:
x - 2 + x/x + 1 - 1/x = -1
x - 2 + x/x + 1 - 1/x = x - 1/x:
x - 1/x = -1
Bring x - 1/x together using the common denominator x:
(x^2 - 1)/x = -1
Multiply both sides by x:
x^2 - 1 = -x
Add x to both sides:
x^2 + x - 1 = 0
Add 1 to both sides:
x^2 + x = 1
Add 1/4 to both sides:
x^2 + x + 1/4 = 5/4
Write the left hand side as a square:
(x + 1/2)^2 = 5/4
Take the square root of both sides:
x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
What is the difference written in scientific notation?
Answer:
6.2 × 10⁵
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs £60. What is the cost of a circular table with a radius of 75cm? Show all your working
Answer:
£135 is the correct answer.
Step-by-step explanation:
Let C be the cost of table.
And let R be the radius of table.
Cost of table is directly proportional to square of radius.
As per question statement:
[tex]C\propto R^{2}[/tex] or
[tex]C=a\times R^2 ....... (1)[/tex]
where [tex]a[/tex] is the constant to remove the [tex]\propto sign[/tex].
It is given that
[tex]C_1 =[/tex] £60 and [tex]R_1 = 50\ cm[/tex]
[tex]C_2 = ?[/tex] when [tex]R_2= 75\ cm[/tex]
Putting the values of [tex]C_1[/tex] and [tex]R_1[/tex] in equation (1):
[tex]60=a \times 50^2 ....... (2)[/tex]
Putting the values of [tex]C_2[/tex] and [tex]R_2[/tex] in equation (1):
[tex]C_2=a \times 75^2 ....... (3)[/tex]
Dividing equation (2) by (3):
[tex]\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135[/tex]
So, £135 is the correct answer.
The cost of 4kg of Apple and 6kg of orange is Rs620.If the cost of orange is the same as the cost of 5 kg Apple find the cost of per kg of Apple and orange?
Answer:
The apple cost RS 18.24 per kg, while
the orange cost RS 91.18 per kg.
Step-by-step explanation:
Let the cost of 1kg if apple and orange be RS A and RS O respectively.
From the first line:
4A +6O= 620
2A +3O= 310 -----(1) (÷2 throughout)
From the information given in second line:
O= 5A -----(2)
subst. (2) into (1):
2A +3(5A)= 310
2A +15A= 310 (expand)
17A= 310 (simplify)
A= 310 ÷17 (÷17 on both sides)
A= 18.235 (5 s.f.)
A= 18.24 (2 d.p.)
Subst. into (2):
O= 5(18.235)
O= 91.18 (2 d.p.)
the sum of three consecutive odd numbers. is 63. ¿what is the smalles of these numbers?
Answer: The answer is 19
Step-by-step explanation:
angle x is coterminal with gale y. if the measure of angle x is greater than the measure of angle y which statement is true regarding the values of x and y
Answer:
The answer is C
Step-by-step explanation:
did the quiz
Answer:
He is right it C just did the quiz let him have the brainly ;)
Step-by-step explanation:
For a hyperbolic mirror the two foci are 42 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus is 36 cm. Position a coordinate system with the origin at the center of the hyperbola and with the foci on the y-axis. Find the equation of the hyperbola.
Answer:
[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]
Step-by-step explanation:
For a hyperbolic mirror the two foci are 42 cm apart.
The distance between the foci = 2c.
Therefore:
2c=42c=21The distance of the vertex from one focus = 6 cm
The distance of the vertex from the other focus = 36 cm
2a=36-6=30
a=15Now:
[tex]c^2=a^2+b^2\\21^2=15^2+b^2\\b^2=21^2-15^2\\b^2=216\\b=6\sqrt{6}[/tex]
If the transverse axis lies on the y-axis, and the hyperbola is centered at the origin. Then the hyperbola has an equation of the form:
[tex]\dfrac{y^2}{a^2} -\dfrac{x^2}{b^2}=1[/tex]
Therefore, the equation of the hyperbola is:
[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]
if f(x)=ln(sin(2x)), f''(π/4) is equal to
Use the chain rule to compute the second derivative:
[tex]f(x)=\ln(\sin(2x))[/tex]
The first derivative is
[tex]f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}[/tex]
[tex]f'(x)=2\cot(2x)[/tex]
Then the second derivative is
[tex]f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'[/tex]
[tex]f''(x)=-4\csc^2(2x)[/tex]
Then plug in π/4 for x :
[tex]f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4[/tex]
Which graph shows exponential growth?
The answer is graph A 7/9/20 edge
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Simplify
20x over 70x
Answer:
The answer is 2/7.
Step-by-step explanation:
You have to cut out the common terms :
[tex] \frac{20x}{70x} [/tex]
[tex] \frac{20}{70} [/tex]
[tex] \frac{2}{7} [/tex]
Quinn used a scale drawing to build a soccer field near his school. Initially, he wanted the field to be 28 yards long and 17.5 yards wide. He decided to change the length of the field to 36 yards.
If the width is to be changed by the same scale factor, what is the new width of the field? Express your answer to the nearest tenth.
18.5
22.5
25.5
57.6
Answer:
So the answer is going to be B. AKA 22.5
Step-by-step explanation:
I took the test on ed and got this answer right! hth (hope this helps)
Answer:
B, second option, 22.5
Step-by-step explanation:
1.)because
2.)i'm
3.)kinda
4.)smart
answer=22.5:))))))))
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. x = 5.22 5.69 6.25 6.75 7.25 y 17 12 33 37 62What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? a. 95.7% b. 0.7% c. 8.4% d. 91.6% e. 4.3%
Answer:
(B) 0.7%
Step-by-step explanation:
X = Land Elevation (in ,000 feet)
Y = Unidentified Artifacts (in %)
The hypothetical theory says that:
The higher the elevation, the higher the percentage of unidentified artifacts in the location.
To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.
Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.
Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%
During your journey, you develop an abscessed tooth and have to visit the dentist. You are prescribed an antibiotic with a dosage of 7.5 mg/kg every six hours. If you weigh 128 pounds and the antibiotic comes in 250 mg tablets, how many tablets should you take each day?
Answer:
I should take 10.44 tablets in a day, approximately 10.5 tablets.
Step-by-step explanation:
In order to solve this problem we need to convert the weight from pounds to kilograms, to do that we need to divide it by 2.205.
[tex]w = \frac{128}{2.205}\\w = 58.05 \text{ kg}[/tex]
Since I need to take 7.5 mg per kg of body weight, then in order to find the dosage we need to multiply the weight in kg by 7.5.
[tex]\text{dosage} = 58*7.5 = 435 \text{ mg}[/tex]
Since I need to take it every six hours and there are 24 hours in a day, we will have to take 4 dosages in a day, therefore we need:
[tex]\text{dosage(day)} = 435*6 = 2,610 \text{ mg}[/tex]
The antibiotic comes in 250 mg in tablets, therefore the number of tablets is:
[tex]tablets = \frac{2610}{250} = 10.44[/tex]
I should take 10.44 tablets in a day, approximately 10.5 tablets.
In a random sample survey 75 people at a high school football game 60 people said that they wanted the home team to win there a total of 600 people at the football game how many people would predict do you want the home team to win based on the survey
Answer:
480
Step-by-step explanation:
Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total
Answer:
Answer: 4615.66667
Steps: 1 foot=0.33333
total feets=30.5×454=13847
13847 feets=46.1566667 yards
The result of which expression will best estimate the actual product of (-4/5)(3/5)(-6/7)(5/6)
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{-4}{5} * \frac{3}{5} * (\frac{-6}{7} ) * \frac{5}{6}[/tex]
[tex]\frac{(-4) * 3}{5 * 1} * \frac{(-1)}{7} \\\\\frac{12}{35}[/tex]
Solve 2cos3x=0.9.
Pls help me with this trigonometric equations
Step-by-step explanation:
Simplifying
f(x) = 2cos(3x)
Multiply f * x
fx = 2cos(3x)
Remove parenthesis around (3x)
fx = 2cos * 3x
Reorder the terms for easier multiplication:
fx = 2 * 3cos * x
Multiply 2 * 3
fx = 6cos * x
Multiply cos * x
fx = 6cosx
Solving
fx = 6cosx
Solving for variable 'f'.
Move all terms containing f to the left, all other terms to the right.
Divide each side by 'x'.
f = 6cos
Simplifying
f = 6cos
Solve for x
A) -8
B) 3.5
C) 8
D) 26
Answer:
C) 8
Step-by-step explanation:
By remote interior angle property of a triangle.
[tex] 19x - 3 = 94° + 7x - 1\\\\
19x - 7x = 94 + 3 - 1\\\\
12 x = 96\\\\
x = \frac{96}{12}\\\\
\huge \orange{\boxed {x = 8}} [/tex]
please hurry I’ll make brainiest
A ball is tossed into the air from a height of 6 feet above ground level,
with a velocity of 3.4 feet per second. Which function could be used to
model the height of the ball, after t seconds?
Answer:
I think it would be the first but not 100% sure
Step-by-step explanation:
The volume of this prism
[tex]answer = 66 \: {cm}^{3} \\ solution \\ volume = lwh \\ \: \: \: \: \: \: \: \: \: \: = \: 11 \times 3 \times 2 \\ \: \: \: \: \: \: \: \: \: = 66 \: {cm}^{3} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
[tex]= 66 {cm}^{3} \\ [/tex]
Step-by-step explanation:
[tex]volume = base \times length \times height \\ = 3cm \times 11cm \times 2cm \\ = 66 {cm}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The tree diagram below shows all of the possible outcomes for flipping three coins.
What is the probability of one of the coins landing on tails and two of them landing on heads?
A) 1/4
B) 3/8
C) 1/2
D) 3/4
Answer:
B
Step-by-step explanation:
In that scenario, you would have one T and two H's, in any order. Looking at the chart, this happens in 3 different scenarios. Since there are a total of 8 possible outcomes, the probability of this happening is 3/8 or answer choice B. Hope this helps!
Answer:B
Step-by-step explanation: the number of event is 3 event={HHT, HTH,THH }
And the number of sample space is 8
By using 2^n formula our n is 3 2^3 = 8
The probability = 3/8
Hope it helps
Brainliest please
An item has a listed price of 90$. If the sales tax rate is 6% how much is the sales tax (in dollars)?
Answer:
five dollars and forty cents
5.40$
Step-by-step explanation:
90+6%= 95.40
Draw a model of square root of 12 using perfect squares
Answer:
The answer is "[tex]\sqrt{12}[/tex] is not a perfect square".
Step-by-step explanation:
12 is not a perfect square because it is the natural number, and no other natural number would square the number 12, that's why it is not a perfect square.
If we calculate the square root of [tex]\sqrt{12}[/tex]. so, it is will give [tex]2\sqrt{3}[/tex] that is not a perfect square root which can be described as follows:
[tex]\Rightarrow \sqrt{12}= \sqrt{2\times 2\times 3}[/tex]
[tex]= \sqrt{2^2\times 3}\\\\= 2\sqrt{3}\\\\[/tex]
[tex]\bold{\sqrt{12}}[/tex] is not a perfect square root.
Answer:
Here's a picture
Step-by-step explanation:
What is the slope of a line that is parallel to the line y =3/4 x + 2?
a. -4/3
b. -3/4
c. 3/4
d. 4/3
Answer:
The answer is C, 3/4.
Since it is parallel to y=3/4 x+2, 3/4 is the slope for both equations.
Which type of symmetry?
Answer:
both rotational and reflectional
Answer: both rotational and reflectional
Step-by-step explanation: a p e x
A = (5,2), B = (2,4), C = (6,7) and D = (9,5) What is the length of the shorter diagonal of parallelogram ABCD?
Answer:
[tex] AC = \sqrt(26) \approx 5.1 [/tex]
Step-by-step explanation:
The diagonals are AC and BD.
Now we find the lengths of the diagonals using the distance formula.
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
AC:
[tex] AC = \sqrt{(6 - 5)^2 + (7 - 2)^2} [/tex]
[tex] AC = \sqrt{(1)^2 + (5)^2} [/tex]
[tex] AC = \sqrt{1 + 25} [/tex]
[tex] AC = \sqrt{26} [/tex]
BD:
[tex] BD = \sqrt{(9 - 2)^2 + (5 - 4)^2} [/tex]
[tex] BD = \sqrt{(7)^2 + (1)^2} [/tex]
[tex] BD = \sqrt{49 + 1} [/tex]
[tex] BD = \sqrt{50} [/tex]
Since sqrt(26) < sqrt(50), then the shorter diagonal is AC.
Answer: AC = sqrt(26) or approximately 5.1
Answer:
A = (5.2)
Step-by-step explanation:
c2= (6-5)^2 + (7-2)^2
To find AC we calculate within parenthesis (6-5) : 1
c2= 1 + (7-2)^2
calculate within parenthesis (7-2) : 5
c2 = 1^2 + 5^2
then calculate exponents 1^2:1
c^2 = 1+5^2
add and subtract left to right
c^2 = 1+25
c^2 =26
Sr of 26 = 5.09901951359
Which means the closest answer is A = 5.2
To find BD we calculate within parenthesis (9-2):7
c2= (9-2)^2 + (5 - 4)^2
calculate within parenthesis (5-4) : 1
c2 = (7)^2 + (1)^2
calculate exponents 1 ^2 : 1
c2 = 49 +1
add and subtract left to right
c2 = 50
Sr of 50 = 7.07106781187
What is the slope of a line that is perpendicular to the line y = x + 5?
Answer:
-1.
Step-by-step explanation:
The standard form of a line can be written y = mx + b where m is the slope.
y = x + 5 can be written as y = 1x + 5 which shows that the slope is 1.
If the slope of a line is m then the slope of a line perpendicular to it is -1/m.
So the required slope is -1/1 = -1.
Answer:
-1
Step-by-step explanation:
the line is exactly opposite like a mirror image when it is perpendicular,
so the gradient of the first line is 1 (because there is no number beside x, the gradient would be 1), that means the opposite of 1 would be -1.
The answer is -1
