X is the number of songs and Y the number of pics
our 2 equations will be - X+y=11 & 4x+2y=24
consider x=11-y
Lets replace x in 2:
=4(11-y) +2y=24
=44-4y+2y=24
=44-24= 4y-2y
=20= 2y
=Y=20/2
=Y=10
Lets replace y in 1
=X+10=11
=X=11-10
=X=1
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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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Use the following recipe to answer questions 1 through 4:
Pumpkin- 1.2 kg
Chicken stock- 1.5L
Sugar- 5 mL
Yogurt- 0.25 L
1)what would be the best u.s standard unit in which to measure the pumpkin?
2) To measure the stock?
3) to measure the sugar?
4) to measure the yogurt?
#1
The unit is pounds
1kg=2.2lbs1.2kg=1.2(2.2)=2.64lbs#2
The unit must be pintSo
1L=2pints(Approx)1.5L=1.5(2)=3pints#3
We shall use cups
1mL=0.004cups5ml=0.020=0.02cups#4
We should use pints
1L=2pints0.25L=2/4=1/2=0.5pintsAnswer:
1. pounds (lb)
2. pints (pt)
3. teaspoon (tsp)
4. cups (c)
Step-by-step explanation:
US Standard UnitsLiquid
Fluid Ounces (fl oz)Cups (c)Pints (pt)Quarts (qt)Gallons (gal)128 fl oz = 16 cups = 8 pints = 4 quarts = 1 gallon
Mass
Ounces (oz)Pounds (lb)Tons (short ton)32000 ounces = 2000 pounds = 1 ton
Solutions1. The best US standard unit in which to measure pumpkin with a mass of 1.2 kg would be pounds (lb).
⇒ 1 kg ≈ 2.205 lb
⇒ 1.2 kg ≈ 1.2 × 2.205 = 2.65 lb
2. The best US standard unit in which to measure stock with a volume of 1.5 L would be pints (pt).
⇒ 1 L ≈ 2.133 pt
⇒ 1.5 L ≈ 1.5 × 2.113 = 3.17 pt
3. The best US standard unit in which to measure sugar of 5 mL would be teaspoon (tsp).
⇒ 5 mL = 5 g ≈ 1 teaspoon
4. The best US standard unit in which to measure yogurt with a volume of 0.25 L would be cups (c).
⇒ 1 L ≈ 4.167 c
⇒ 0.25 L ≈ 0.25 × 4.167 = 1.04 c
In order to play at the Mt. Guinea Country Miniature Golf Club, a player has to pay the membership fee and pay for each round played. The total
cost is represented by the function
T-44.09r+12.70, where T the total cost (in dollars) and r= the number of rounds played.
Which of the following statements must be true?
Calculate a central angle in degree intercepting an arc of length 7 pi/2 cm in a circle with radius 77cm.
The arc length of the circle exists 846.65922 cm.
How to estimate the central angle in degree?
A unit circle by definition contains a radius of 1 unit.
We have to estimate the length of the arc subtended by an angle of [tex]7\pi/2[/tex] radians.
arc length = radius [tex]*[/tex] angle
s = r[tex]$ * \theta[/tex]
Where s be the arc length
r be the radius of the circle
[tex]\theta[/tex] be the angle measured in radians
arc length = 77cm[tex]$*7\pi/2[/tex]
arc length = 77 [tex]*[/tex] 7(3.14) / 2
arc length = 846.65922 cm
Therefore, the arc length of the circle exists 846.65922 cm.
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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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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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Kim has $10$ identical lamps and $3$ identical tables. How many ways are there for her to put all the lamps on the tables
There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables
How to determine the number of ways?The given parameters are:
Identical lamps, n = 10Identical tables, r = 3The combination involving identical objects is calculated using:
(n + r - 1)C(r - 1)
So, we have:
n + r - 1 = 10 + 3 - 1
Evaluate the sum
n + r - 1 = 13 - 1
Evaluate the difference
n + r - 1 = 12
Also, we have:
r - 1 = 3 - 1
Evaluate the difference
r - 1 = 2
So, we have:
(n + r - 1)C(r - 1) = 12C2
Apply the following combination formula:
nCr = n!/((n - r)!r!)
So, we have:
12C2 = 12!/((12 - 2)! * 2!)
Evaluate the difference
12C2 = 12!/(10! * 2!)
Expand the numerator
12C2 = 12 * 11 * 10!/(10! * 2!)
Evaluate the quotient
12C2 = 12 * 11/2!
Expand the denominator
12C2 = 12 * 11/2 * 1
Evaluate the product
12C2 = 132/2
Evaluate the quotient
12C2 = 66
Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables
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Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
What is the distance?Distance is a measurement of time and speed.
The distance equals speed multiplied by time.
Data and Calculations:Distance between Alice and Bob = 1,000 feet
Distance between the bird and Bob = 1,000 feet
Speed of Alice and Bob = 10 feet per second, respectively
The combined speed of Alice and Bob = 20 feet per second
Since the two are running directly toward each other, the distance each will cover at the meeting point is 50 feet (1,000/20)
The time covered at the meeting point = 20 seconds (1,000/50)
Speed of the bird = 20 feet per second
The distance covered by the bird towards Bob at their meeting point is 40 feet (20 feet x 20 seconds)
Thus, the total distance covered by the bird at the meeting point is 40 feet.
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Adam’s house is 2 centimeters from juan’s house on a map. if each centimeter on the map represents 6 kilometers, how far apart are the two houses? startfraction 1 over 12 endfraction kilometer one-third kilometer 3 kilometers 12 kilometers
Juan's home is about 12 kilometers from Adam's.
What are measurements in math's?In the study of mathematics and science, measurement is the fundamental idea. By quantifying an object's or event's qualities, we can compare them to those of other objects or occurrences. When discussing the division of a quantity, the phrase "measurement" is most frequently employed.
According to the given information:The distance between Adam's and Juan's residences on the map in centimeters is simply multiplied by the number of kilometers that each centimeter on the map represents, which in this case is 6, to determine how far Adam's house is from Juan's.
2 * 6 = 12
Which is our response.
Juan's home is about 12 kilometers from Adam's.
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Geometry: ASAP!!! Complete this proof
Answer:
1. ∠1 ≅ 6 : Given
2. ∠3 ≅ ∠ 4 : Vertical Angles Congruence Property
3. ∠2 ≅ ∠5 : Corollary III of Theorem 19 : If two angles of two triangles are congruent, then the third angle of both triangles are congruent.
Step-by-step explanation: For ∠3 ≅ ∠4, the angles are in a diagonal placement, meaning they are vertical angles. Vertical angles are always congruent.
Lookimg at one of the problems you posted earlier, the Corollary III of Theorem 19 given, states that if two angles are congruent in both triangles, then the third angle is congruent in both triangles. Since we have 2 angles already congruent to 2 other angles, ∠2 and ∠5 must be congruent.
Hope this helped!
What is the domain of the exponential function shown in the graph?
A.x > -1
B.x ≤ -1
C. x < 0
D. -∞ < x < ∞
The domain of the exponential function shown in the graph is -oo < x < oo
How to determine the domain of the exponential function shown in the graph?The function on the graph is an exponential function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -oo < x < oo
Hence, the domain of the exponential function shown in the graph is -oo < x < oo
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(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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PLEASE HELP IM STUCK
Direct variation is modeled by the equation y = kx, where k is a constant and x and y vary based on the other's value.
We'll first need to find k, also known as the constant of variation, using our given values of x and y.
6 = k * -7
k = -6/7
Now that we have k, we can plug it in and substitute other values in for x or y. In this case, we'll plug in 4 for x and solve for y.
y = -6/7x
y = -6/7 * (4)
y = -24/7
y = -24/7
Hope this helps!
Answer:
y = -24/7
Step-by-step explanation:
We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.
When y = 6, x = -7, so the proportion will be 6 : -7.
We need to find the y when x is 4, so our equation will be:
6 : -7 = y : 4
Since the proportion will be the same.
Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.
-7y = 24
y = 24 / -7
y = - 24/7
So y = -24/7 will be our answer!
+ Since the '-' is already written down, the top box will contain 24, and the bottom box will contain 7.
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
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)
Is the following number rational or irrational [tex]Is the following number rational or irrational \sqrt{45\\}[/tex]
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]
If x + y = x, show that x = 1.
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
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
CAN SOMEONE HELP ASAP WITH 7,8?!!??!
For triangle DEF,
m∠D = 21°
m∠E = 87°
DF = 16
For triangle RST,
m∠S = 68°
m∠T = 57°
Simple polygons with three sides and three internal angles make up triangles. It is one of the fundamental geometric shapes in which the three vertices are connected to one another.
For ΔDEF, it is given that, m∠F = 72°, DE=15,EF=17.
By the law of cosines,
side DF=(a2+b2﹣2abcosγ)1/2
DF=16
Similarly,
m∠D = 21°
As the sum of angles of triangle is 180,
m∠E = 87°
For ΔRST, it is given that, m∠R = 55°, RS=17,RT=9.
By the law of cosines,
side ST=(a2+b2﹣2abcosγ)1/2
ST=16
Similarly,
m∠S = 68°
As the sum of angles of triangle is 180,
m∠T = 57°
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Choose the inverse of y=x²-10x.
Oy=±√√x-25-5
O y = ± √√x-25 +5
Oy=√x+25-5
Oy=+√√x+25 +5
Answer:
[tex]y = \sqrt{x+25} + 5[/tex]
Step-by-step explanation:
Swap x and y
x = y² – 10y
Add 25 to each side to complete the square
x + 25 = y² – 10y + 25
Factor
x + 25 = (y – 5)²
Take the square root of each side
[tex]\sqrt{x+25}[/tex] = y – 5
Add 5 to both sides
[tex]\sqrt{x+25}[/tex] + 5 = y
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)
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]
Kari is preparing for a party and must have the perfect outfit with one
jacket and one jumpsuit. How many possible outcomes can she create if
she has a jean jacket, leather jacket, white jumpsuit, tan jumpsuit, green
jumpsuit, and a black jumpsuit?
Answer:
8
Step-by-step explanation:
Kari has 2 choices for jackets and 4 choices for jumpsuits. We'll multiply those together to find the number of options she has.
Since the numbers are very small, we can grind out this same number (but be organized):
Jean/white
Jean/tan
Jean/green
Jean/black
Leather/white
Leather/tan
Leather/green
Leather/black
These are the eight choices.
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]
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.
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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Lakisha’s employer pays $2,150 in health insurance and $86 in life insurance per year. she also gets $3,520 in paid time off per year. her monthly gross pay is $4,370. what are lakisha’s total job benefits per year? a. $5,756 b. $10,126 c. $52,440 d. $58,196 please select the best answer from the choices provided a b c d
Lakisha's total job benefits per year are (D) $58,196.
What are employees' benefits?Employee perks and benefits in kind are non-wage compensation provided to employees in addition to their regular income or salary. A "salary package" or "salary exchange" arrangement is one in which an employee exchanges salaries for some other type of compensation.To find Lakisha's total job benefits:
If Lakisha's employer pays $2,150 in health insurance and $86 in life insurance per year, and she also gets $3,520 in paid time off per year, then Lakisha's total job benefits per year are equal to:
Total Benefits = Health Insurance + Life Insurance + Paid Time Off + Annual Gross Pay
Total Benefits= $2,150+$86+$3,520+12($4,370)Total Benefits= $2,150+$86+$3,520+$52,440Total Benefits=$58,196Therefore, Lakisha's total job benefits per year are (D) $58,196.
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Answer The answer is D
Step-by-step explanation:
I got it correct on edg