Answer:
Step-by-step explanation:
20 liters -1 liter = 19 liters of milk
20 liters -1 liter = 19 liters of syrup
This was done twice so therefore;
19 liters -1 liter = 18 liters of milk
19 liters -1 liter = 18 liters of syrup
Therefore the ratio comes to 18:18
18 goes into 18 1 and the same for the other 18. Therefore the ratio comes to ;
1:1
Your final answer is 1:1
HELP WITH THE BONUS PLEASE!!!!
Based on the stock price and its growth rate, the function that models the situation is 48 (1 + 8%) ^ n. The price of the stock 6 years from now is $76.17.
What is the best function for the stock's growth?The value of a stock in future can be calculated using several types of formulas that take into account the various characteristics of the stock.
For this stock, the value of the stock at any given year is:
= Current price of stock x ( 1 + growth rate) ^ number of years from now
Assuming the number of years is n, the function becomes:
= 48 x ( 1 + 8%) ^n
In 6 years, the price will be:
= 48 x ( 1 + 8%) ⁶
= $76.17
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Let S1 be the amount allowing 10% discount on the price of some goods and then adding 10% VAT. Let S2 be the amount adding 10% VAT and then allowing 10% discount. Which of the following is true? (i) S1 > S2 (ii) S1 < S2 (iii) S1 = S2 (iv) Cant be decided
Using decimal multipliers, the correct statement is given by:
(iii) S1 = S2.
What is a decimal multiplier?Increases of a% or decreases of a% re represented by decimal values, as follows:
The equivalent multiplier for an increase of a% is given by: [tex]\frac{100 + a}{100}[/tex]The equivalent multiplier for an decrease of a% is given by: [tex]\frac{100 - a}{100}[/tex]Hence, in the context of this problem:
An increase of 10% is represented by 1.1.A decrease of 10% is represented by 0.9.The options are given as follows:
S1 = 0.9 x 1.1 = 0.99.S2 = 1.1 x 0.9 = 0.99.They are equal, hence option (iii) is correct.
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If you eat a diet with 2,000 kilocalories and 45 percent of those calories come from protein, about how many grams of protein did you eat?
The amount of Protein intake is 900 kilocalorie.
We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.
Wе have to find out the amount of protein intake.
If ' x ' students out of total ' n ' students in a class are infected by virus. Then, what percentage of students are infected.Percentage of students affected are - [tex]\frac{x}{n} \times 100[/tex]
In the question given -
Let the amount of Protein intake be y.
Then -
45 = y % of 2000
45 = [tex]\frac{y}{2000} \times100[/tex]
y = [tex]\frac{45\times2000}{100}[/tex]
y = 900 Kilocalorie
Hence, the amount of Protein intake is 900 kilocalorie.
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Hans is planting a garden with snapdragons and daisies. the table shows some possible combinations of the two plants. if hans plants 29 daisies, how many snapdragons will he plant?
The linear equation y = -x+45 models the scenario.
Solving the linear equation, it exists found that Hans will paint 16 snapdragons.
What is linear equation?Since the rate of change exists always the exact, this question exists modeled by a linear equation.
Linear equation: y = mx + b
Where, m exists the slope and b exists the y-intercept.
To find the slope, we have to get two points (x, y), and the slope exists given by the change in y divided by the change in x.
Points: (11, 34) and (12, 33).
Change in y: 33 - 34 = -1
Change in x: 12 - 11 = 1.
Slope: m = -1/1 = -1
The equation of the line exists y = -x + b
Replacing one of the points, the y-intercept can be found.
Point (11, 34) means that when x = 1, y = 34.
y = -x + b
34 = -1+b
b = 45
Therefore, the equation y = -x+45 models the scenario.
29 daisies mean that y = 29, we have to estimate the value of x for which y = 29.
y = -x+45
simplifying the equation,
29 = -x+45
x = 45 - 29 = 16
The value of x = 16
Therefore, Hans will plant 16 snapdragons.
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Answer:
The equation ✔ x = 45 – y models the scenario.
Hans will plant✔ 16 snapdragons
Step-by-step explanation:
Consider the quadratic function f(x)=x²-5x+12. Which statements are true about the function and its
graph? Select three options.
A. The value of f(-10) = 82
B. The graph of the function is a parabola.
C. The graph of the function opens down.
D. The graph contains the point (20,-8).
E. The graph contains the point (0, 0).
There is only one statement that is true: B. The graph of the function is a parabola.
How to study and interpret the characteristics of quadratic equations
In this question we have a quadratic equation, whose characteristics have to be inferred and analyzed. We need to prove each of the five choices presented in the statement:
Choice A:
If we know that x = - 10, then we evaluated it at the function:
f(- 10) = (- 10)² - 5 · (- 10) + 12
f(- 10) = 162
False
Choice B:
By analytical geometry we know that all functions of the form y = a · x² + b · x + c always represent parabolae.
True
Choice C:
The quadratic function opens up as its leading coefficient is greater that 0.
False
Choice D:
If we know that x = 20, then we evaluate it at the function:
f(20) = 20² - 5 · (20) + 12
f(20) = 312
False
Choice E:
If we know that x = 0, then we evaluate it at the function:
f(0) = 0² - 5 · (0) + 12
f(0) = 12
There is only one statement that is true: B. The graph of the function is a parabola.
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Factorise :
ab(x^2 - y^2) + (a^2 - b^2)xy = 0
Step-by-step explanation:
abx^2-aby^2+xya^2-xyb^2
abx^2+xya^2-aby^2-xyb^2
ax(bx+ya)-yb(ay+xb)
ax(bx+ya)-yb(xb+ay)
(ax-yb) (bx+ya)
If x + y = x, show that x = 1.
4. The figure shows a rectangular tank.
(a) The capacity of the tank is ___ L.
(b) After pouring 10L of water into the tank, the depth of water will be __ cm.
Answer:
20 L volume and 12.5 cm depth.
Step-by-step explanation:
See attached image.
3. The function defined by m(h) = 300 * (3/4) ^ h represents the amount of a medicine, in milligrams, in a patient's bodyrepresents the number of hours after the medicine is administered . a. What does m(0.5) represent in this situation?
This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.
What does m(0.5) represent in this situation?We know that the exponential function defined by:
[tex]m(h) = 300*(3/4)^h[/tex]
Represents the amount of a mediciene, in milligrams, after a number of hours h.
We want to see what does m(0.5) represent. This is the exponential function evaluated in h = 0.5
Then, it just represents the amount of medicine, in miligrams, in a patient's body present 0.5 hours after the medicine was administered.
Replacing h = 0.5 we get:
[tex]m(0.5) = 300*(3/4)^{0.5} = 259.81[/tex]
This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.
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BC is tangent to circle A at point B.
Find m/CAB if m/ACB=62".
Enter your answer in the box.
m/CAB
Answer:
28
Step-by-step explanation:
Tangent is a line that touches the circle at one point and is perpendicular to the radius. Circle A has radius AB and tangent CB, so AB is perpendicular to CB. Therefore triangle ABC is a right angle, with angle B measuring 90 degrees. Since interior angles of a triangle add up to 180 degrees, measure of angle A is 180 - 90 - 62 = 28 degrees.
Is the following number rational or irrational [tex]Is the following number rational or irrational \sqrt{45\\}[/tex]
Adult men have heights with a mean of 69. 0 inches and a standard deviation of 2. 8 inches. find the z-score of a man who is 71. 9 inches tall. (to 4 decimal places)?
The value of the z score is 1.03.
According to the statement
we have given that the value of mean and standard deviation and we have to find the value of the z score.
So, For this purpose we know that the
Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
And the given values are:
mean value = 69 inches
s.d value = 2.8 inches
And the value of x is 71.9 inches.
So, The Z score is
z = x - mean / standard deviation
substitute the values in it then
z = 71.9 - 69 / 2.8
then
z = 2.9 /2.8
z = 1.03
So, The value of the z score is 1.03.
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What is the answer ?
∠ADB + ∠BDC = ∠ADC
39° + (3x - 4) = 8x + 5
3x - 4 = 8x + 5 - 39
3x - 4 = 8x - 34
34 - 4 = 8x - 3x
5x = 30
x = 6
∠ADC = 39° + (3(6) - 4) = 39 + 14 = 53°
Hope it helps!
Express the volume of the box as a
polynomial in the variable x
The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
How to determine the volume?The complete question is added as an attachment
From the attached image, we have:
Length = 12 - 2x
Width = 7 - 2x
Height = x
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
Volume = (12 - 2x) * (7 - 2x) * x
This gives
Volume = x(12 - 2x)(7 - 2x)
Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
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Emma learned in science class that fruit fly populations can increase by about 30% each day.
She found 7 fruit flies on a rotten banana today, and she is curious how many fruit flies could
be on the banana in a few days. You can use a function to approximate the number of fruit
flies on the banana after x days.
Write an equation for the function. If it is linear, write it in the form h(x) = mx + b. If it is
exponential, write it in the form h(x) = a(b)*.
h(x) =
DIO
89
Answer:
[tex]h(x)=7(1.3)^x[/tex]
Step-by-step explanation:
Since this is an exponential equation we will use
[tex]h(x)=a(b)^x[/tex]
[tex]a[/tex] Is your starting value, 7
[tex]b[/tex] Is your percentage of change, remember its not 0.3, as that would hint the population is decreasing by thirds exponentially, instead we will use 1.3 as our percent of change, as the 1 maintains the original value and the 0.3 adds 30%, now all we have to do is put it all together!
[tex]h(x)=7(1.3)^x[/tex]
You are given an expression for the volume of the rectangular prism. determine an expression for the missing dimension. v=4x^3 5x^2-32x-33 and the dimensions are (x 1)and (x 3)
Find the equation of a line in slope-intercept form with a slope of 5 that contains the point (3,8).
Group of answer choices
y=5x−15
y=5x+8
y=5x−7
y=3x+8
Answer:
y = 5x - 7
Step-by-step explanation:
y = mx + c
y = 5x + c
to find c, input given coordinates
8 = 5 x 3 + c
8 = 15 + c
-c = 15 - 8
-c = 7
c = -7
put that all together and you get:
y = 5x - 7
The equation of the line with a slope of 5 that contains the point (3,8) is
y = 5x - 7.How to find the equation of the lineThe equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the slope is 5 and the line contains the point (3,8), we can substitute these values into the equation and solve for the y-intercept (b).
Using the point-slope form of the equation:
y - y₁ = m(x - x₁)
We have:
y - 8 = 5(x - 3)
Expanding and simplifying:
y - 8 = 5x - 15
Now, let's isolate y:
y = 5x - 15 + 8
y = 5x - 7
Therefore, the equation of the line with a slope of 5 that contains the point (3,8) is y = 5x - 7.
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A rectangular prism with a volume of 3x^3+16x^2+5x cubic units has a base area of x^2+5xsquare units. Find the height of the rectangular prism.
The height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.
Volume of rectangular prismVolume of the prism = 3x³ + 16x² + 5x cubic unitsBase area = x² + 5x square unitsVolume of a rectangular prism = Base area × height
Height = Volume of a rectangular prism ÷ Base area
3x³ + 16x² + 5x cubic units = (x² + 5x) square units × h
h = (3x³ + 16x² + 5x) cubic units ÷ (x² + 5x) square units
h = (3x³ + 16x² + 5x) / (x² + 5x) units
Therefore, the height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.
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Armando used algebra tiles to represent the product 3 x (2 x minus 1). an algebra tile configuration. 3 tiles are in the factor 1 spot and are labeled x. 3 tiles are in the factor 2 spot: 2 are labeled x and 1 is labeled negative. 15 tiles are in the product spot: 2 are labeled x squared, 4 are labeled x, 1 is labeled negative x, and 4 are labeled negative. which is true regarding armando’s use of algebra tiles?
The correct powers of x are not displayed in several of the goods.
What is algebraic tiles?Algebra tiles are mathematical manipulatives that help pupils better comprehend algebraic thinking and its ideas. These tiles have shown to give beginning algebra pupils in elementary, middle, high, and college concrete models.
How do algebraic tiles function?Blocks called algebra tiles can be used to symbolize constant, linear, and quadratic terms. Small yellow squares stand in for constant blocks, green rectangles for linear blocks, blue squares for quadratic blocks, and red squares for negative sides for all other types of blocks.
Future:
The image shows,
3x(2x - 1) = 6x² - 3x
This should be the appropriate representation on the tile:
_____+x _____ +x _____ +x
+x _ +x² ______+x² ______+x²
|
+x__ +x² _____ +x² ______+x²
|
- __ -x ______ -x _______-x
+6x² - 3x
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can you guys pls help
Check the picture below.
so the lateral area of the pyramid is really just the area of four triangles whose base is 10 and height is also 10, now, we're excluding the bottom because that's not lateral area.
[tex]\stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{10}) \right]}\implies 2(100)\implies \text{\LARGE 200}~ft^2[/tex]
d= the square root of 4h/5 make h the subject of the formula
[tex]d = \sqrt{ \frac{4h}{5} } \\ square \: both \: sides \\ d {}^{2} = \frac{4h}{5} \\ multiply \: both \: sides \: by \: 5 \\ 5d {}^{2} = 4h \\ divide \: both \: sides \: by \: 4[/tex]
[tex]h = \frac{5d {}^{2} }{4} [/tex]
A carpenter can install 35 windows in 7 days. how many windows can he install in 15 days
Answer:
84
Step-by-step explanation:
Multiply 35 by 2.5
Answer:
75 windows
Step-by-step explanation:
35 ---- 7
x ----- 15
[tex]x=\frac{(35)(15)}{7} =75[/tex]
Hope this helps
(0,2)(3,686) exponential function
The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The standard form of an exponential funtion is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
At point (0, 2)
2 = ab⁰
a = 2
At point (3, 686)
686 = 2b³
b = 7
The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ
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The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 14, 13, 16, 12, 17, 21, 26
Answer:
Hey stu132057, your the MAD for the data set given is
Step-by-step explanation:
Step 1: Find the mean of the data: (14+13+16+12+17+21+26)/7 = 17
Step 2: Find the difference between each data and mean:Difference between 14 and 17 is 3
Difference between 13 and 17 is 4
Difference between 16 and 17 is 1
Difference between 12 and 17 is 5
Difference between 17 and 17 is 0
Difference between 21 and 17 is 4
Difference between 26 and 17 is 9
Step 3: Add all the differences: 3+4+1+5+0+4+9 = 26
Step 4: Divide it by the number of data:26/7 = 3.7
So, the MAD = 3.7
-------------------------
Have a great day,
Nish
Which answer choice below correctly identifies the 205th term in the sequence 5, 10, 15, 20, 25 …?
Answer:
1025
Step-by-step explanation:
y=5x
y=5(205)
y=1025
The 205th term in the arithmetic sequence is 1025.
We have,
To find the 205th term in the sequence 5, 10, 15, 20, 25 ..., we can use the formula for an arithmetic sequence:
The nth term of an arithmetic sequence can be represented as:
[tex]a_n = a_1 + (n - 1) ~d[/tex]
Where:
[tex]a_n[/tex] is the nth term,
[tex]a_1[/tex] is the first term,
n is the position of the term we want to find, and
d is the common difference between consecutive terms.
In this sequence, the first term [tex]a_1[/tex] is 5, and the common difference (d) is 10 - 5 = 5.
Now, let's find the 205th term ([tex]a_{205}[/tex]):
= 5 + (205 - 1) * 5
= 5 + 204 * 5
= 5 + 1020
= 1025
Thus,
The 205th term in the arithmetic sequence is 1025.
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help
4/10 as a decimal
Answer:
0.4
Step-by-step explanation:
4/10 is 4÷10 = 0.4
5. On the way to the museum, 50% of the students rode on the first bus.
What fraction of the students rode on the second bus? Show your work
in the space below. Remember to check your solution.
Answer:
1/2
Step-by-step explanation:
Since 50% is half the number of students it means that half of the students took the first bus which leaves the other half to take the 2nd bus
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
(6, 1)
(1, 3)
(-7, 6)
Step-by-step explanation:
To have a function, each value used for x can appear only once.
The first set of points has as x: 1, -7, -3.
The only choice without 1, -7, or -3 for x is (6, 1)
The second set of points has as x: 2, 6, -7.
The only choice without 2, 6, or -7 for x is (1, 3)
The third set of points has as x: 1, -3, 6.
The only choice without 1, -3, or 6 for x is (-7, 6)
An art gallery wants to display 4 pieces of art in the front window. if there are 8 pieces to choose from, how many distinct displays are possible?
Answer:
70
Step-by-step explanation:
8 choose 4: 8!/(4!*4!)=70
Answer:
1680
Step-by-step explanation:
the order matters so 8P4
Suppose cos(x) =1/(sqrt(5))
and sin(x) >0. what is the value of tan(2x)?
Answer:
[tex]tan(2\theta) = -\frac{4}{3}\\[/tex]
Step-by-step explanation:
So cos is defined as: [tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex], meaning we can tell that the adjacent side is 1, and the hypotenuse is 5, from the fraction you gave.
Using this we can solve for the opposite side.
[tex]1^2 + b^2 = \sqrt{5}^2\\1+b^2 = 5\\b^2=4\\b=2[/tex]
Now it's important to note, that b can be a negative number, so we have to use the information that sin(x) > 0, to determine the length of this side.
The sin is defined as: [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex], and since we we're solving for the opposite side, this means that the value +\- 2, is in the top, and since the hypotenuse is positive, this means that the opposite side is also positive.
This also tells us one more thing, since both cos(x) and sin(x) are positive, we are dealing with a angle in the first quadrant.
So we can now define sin(x), using the opposite (2) and the hypotenuse (sqrt(5))
[tex]sin(\theta) = \frac{2}{\sqrt{5}}[/tex]
And we can rationalize the denominator for both the cosine and sine, by multiplying by the square root in the denominator so that
[tex]sin(\theta) = \frac{2\sqrt{5}}{5}\\\\cos(\theta) = \frac{\sqrt{5}}{5}[/tex]
Now we can define the value of tan(2 theta) using the double angle-identities such that:
[tex]tan(2\theta) = \frac{2\ tan(\theta)}{1-tan^2{\theta}}[/tex]
And we can also define tan(theta) using the definition that:
[tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]
So plugging in the values sin(theta) and cos(theta) we get the following:
[tex]tan(\theta) = \frac{\frac{2\sqrt{5}}{5}}{\frac{\sqrt{5}}{5}}\\\\tan(\theta) = \frac{2\sqrt{5}}{5} * \frac{5}{\sqrt{5}}\\\\tan(\theta) = 2[/tex]
Btw in the last step, I just canceled out the 5 and sqrt(5) since they were both in the denominator and numerator
So now let's plug this value, 2 as tan(theta) into the equation
[tex]tan(2\theta) = \frac{2\ *2}{1-2^2}\\\\tan(2\theta) = \frac{4}{-3}\\tan(2\theta) = -\frac{4}{3}\\[/tex]