The amount of caffeine in her body on the 1st day is, 2.4 mg
The amount of caffeine in her body on the 2nd day is, 4.8 mg
The amount of caffeine in her body on the 3rd day is, 7.2 mg
Given, Jada drinks a cup of tea every morning at 8:00 am. for 14 days. There is 40 mg of caffeine in each cup of tea she drinks. 24 hours after she drinks the tea, only 6% of the caffeine is still in her body.
So, the amount of caffeine in her body on the 1st day is,
40×6/100
24/10
= 2.4 mg caffeine
The amount of caffeine in her body on the 2nd day is,
= 2× 2.4
= 4.8 mg caffeine
The amount of caffeine in her body on the 3rd day is,
= 3× 2.4
= 7.2 mg caffeine
Hence, The amount of caffeine in her body on the 1st day is, 2.4 mg
The amount of caffeine in her body on the 2nd day is, 4.8 mg
The amount of caffeine in her body on the 3rd day is, 7.2 mg
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Lyle uses a streaming service to watch movies. Last month he paid $26.91 and watched 9 movies. If he watches 11 movies this month, how much will he pay the steaming service?
A. $32.89
B. $26.91
C. $2.99
D. 3.68
Answer:
A. $32.89
Step-by-step explanation:
Take the amount and divide by the number of movies watched
26.91 / 9 =2.99
Now multiply by the new number of movies he wants to watch, 11
2,99 *11
32.89
Answer:
A) $32.89
Step-by-step explanation:
We divided 26.91 by 9 to find how much it is per movie
26.91/9
2.99
It is 2.99 for 1 movie so now we multiply by 11 to find all 11 movies price
2.99x11
$32.89
Hopes this helps please mark brainliest if you would like to learn cross multiply way just let me know
Hello, I really need help this is from ALEKS and I forgot how to solve this. What is 2/3 + 1/5?
Answer:
13/15
Step-by-step explanation:
1. Find a common denominator
2. You always multiply the numerator by the same number as the denominator.
3. then add
In the diagram,ABCD is a rectangular wall that casts a shadow CDEF, on the ground. The wall has a height of 4 feet. The shadow is a parallelogram that has a height, FG, that is twice the height of the wall. If the area of the wall is 29.2 square feet, find the area of the shadow.
We know that the height of the rectangular shape is BC=AD= 4 feet and the the area is A=29.2 ft^2. Since the area of our rectangle is given by
[tex]A=(DC)\times(BC)[/tex]we get
[tex]29.2=DC\times4[/tex]By moving the number 4 to the left hand side, we have
[tex]\begin{gathered} \frac{29.2}{4}=DC \\ \text{then} \\ DC=7.3 \end{gathered}[/tex]which also is the lenght of one side of our parallelogram.
Now, the area of our parallelogram is given by
[tex]A_P=\text{base}\times height[/tex]where the base is given by segment DC=7.3 ft and the height FG=2 BC. Then, we get
[tex]\begin{gathered} A_P=DC\times FG \\ A_P=DC\times2BC \end{gathered}[/tex]by substituting our previous result and BC=4 ft, we obtain
[tex]\begin{gathered} A_P=7.3\times2(4) \\ A_P=7.3\times8 \\ A_P=58.4ft^2 \end{gathered}[/tex]Then, the answer is 58.4 ft^2
Suppose the manufacturer multiplied each side of the
original box by 4. What would the new surface area be?
Answer:
original box wasn't given... atleast send original surface area..
Step-by-step explanation:
^^^^^^!!!!!!!!!!^^^^^^
11. Drew and Nick are selling two different types of raffle tickets for their math club. One
raffle ticket is for a computer and the other is for a gift card. The tickets are different
prices. Drew sells 8 tickets for the computer and 5 tickets for the gift card and receives
$50. Nick sells 8 tickets for the computer and 11 tickets for the gift card and receives
$62. How much does each type of ticket cost?
(52 + 8)------------30solve then write two different word phrases for the expression
Given the expression :
[tex]\frac{52+8}{30}[/tex]To solve the given expression:
First add the numbers 52 and 8 then divide by 30
so, the result will be as following :
[tex]\frac{52+8}{30}=\frac{60}{30}=\frac{6}{3}=2[/tex]So, the answer is : 2
=========================================================
Also, we need two different word phrases for the expression
The first :
52 increased by 8 then divided by 30
The second :
The Quotient of the sum numbers (52 , 8 ) and 30
Reviewrship10These figures are similar. The area ofone is given. Find the area of the other.Help ResourcesArea = 100 in.2ㅁ nSkip8 in.10 in.[? ] in.2Enter
SOLUTION:
Step 1:
Since the two figures are similar, it means that they have properties in common.
Step 2:
In the bigger figure, the side given is 10in and its area is 100 square inches meaning (10 in x 10 in).
Step 3:
In the smaller figure, the side given is 8in, and from step 1, we can see that the two figures are similar, so the area of the smaller figure will be (8 in x 8 in) = 64 square inches.
CONCLUSION:
The area of the smaller figure is 8in x 8in = 64 square inches
[tex]8inx8in=64in^2[/tex]find the circumference and area of the circle round to the nearest whole number
Here, we want to find the circumfrence and area of the circle
To find either of this, we need the value of the radius of the circle
The radius of a circle is the distance btetween the center of the circle and the circumfrence of the circle. In this question, this distance is 20 ft
Mathematically, we can calculate the area with the formula;
[tex]\begin{gathered} A\text{ = }\pi\text{ }\times r^2 \\ A\text{ = }\frac{22}{7}\text{ }\times20^2 \\ \\ A\text{ = }\frac{22\text{ }\times\text{ 400}}{7} \\ \\ A\text{ = 1257.1429} \\ \\ A=1257ft^2\text{ to the nearest whole number} \end{gathered}[/tex]To calculate the circumfrence of the circle, we use the formula below;
[tex]\begin{gathered} C\text{ = 2 }\times\text{ }\pi\text{ }\times\text{ r} \\ \\ C\text{ = 2 }\times\text{ }\frac{22}{7}\text{ }\times\text{ 20} \\ \\ C\text{ = }\frac{880}{7} \\ \\ C\text{ = 125.71} \\ \\ C\text{ = 126 ft to the nearest whole number} \end{gathered}[/tex]Order the values from least to greatest.| -4.3= 4.6= 2.7-35III(1.21
To order the values from least to greatest, we must take into account some important rules, for example.
1.a whole number is greater than a decimal number
2. The greater the decimal number that has more in its integer part.
3.The number placed furthest to the right of the number line is greater. For example +2 is greater than -1. -2 is greater than -3
Now taking into account these rules, we are going to order the numbers given in the exercise from lowest to highest;
-35
-4.3
1.21
2.7
III ;which is equal to 3 integers
4.6
HURRY ASAP!
What is four-twelfths times seven?
Your answer should be in whole or mixed number form.
A. two and four-twelfths
B. 3
C. six and six-sevenths
D. 21
Answer:
A
Step-by-step explanation:
(7 / 12) × 4 = 28 / 12 = 2 and 4 twelfths
There are 17 flute players and 15 Clarinet players in Amy’s Music class, For each class the teacher randomly selects a student to hand out the music by Drawing a name from a jar. What is the probability that a player will be selected to hand out the music for the next class
for this case we have the folloeing information: In a class we have 17 flute players and 15 Clarinet Players for the Amy's Music Class.
The total of students are:
[tex]\text{Total}=17+15=32[/tex]And then if we need to select one player (student) the probability would be given by:
[tex]p=\frac{possible}{total}=\frac{1}{32}[/tex]And the best answer would be A) 1/32
Simplify. Rewrite the expression in the form
[tex] {a}^{n} [/tex]
[tex] {a}^{0} \times {a}^{6} [/tex]
Answer:
[tex]a^{6}[/tex]
Step-by-step explanation:
[tex]a^{0}[/tex] × [tex]a^{6}[/tex] = [tex]a^{0+6}[/tex]
= [tex]a^{6}[/tex]
This is one that I have a lot of trouble with!
Given: The function given are
[tex]\begin{gathered} f(x)=4x^3+5x^2-3x-6 \\ g(x)=4x-5 \end{gathered}[/tex]Required: To find the function-
[tex](f-g)(x)[/tex]Explanation: The function can be determined as follows-
[tex](f-g)(x)=f(x)-g(x)[/tex]Putting the values of the function f(x) and g(x)-
[tex]\begin{gathered} (f-g)(x)=(4x^3+5x^2-3x-6)-(4x-5) \\ =4x^3+5x^2-3x-6-4x+5 \\ =4x^3+5x^2-7x-1 \end{gathered}[/tex]Final Answer: Option A is correct.
Hi, can you answer the second question for me (number 4)?
Solution
4.
[tex]\begin{gathered} \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{cos\theta(1-sin\theta)+cos\theta(1+sin\theta)}{(1+sin\theta)(1-sin\theta)} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{cos\theta-sin\theta cos\theta+cos\theta+sin\theta cos\theta}{1-sin^2\theta} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{2cos\theta}{cos^2\theta} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{2}{cos\theta} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=2sec\theta \end{gathered}[/tex][tex]3/7*14/15*10/18\\[/tex]
The value of the fraction 3/7 × 14/15 × 10/18 is 2/9.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
The value of the fraction will be:
= 3/7 × 14/15 × 10/18
= 3/7 × 14/15 × 5/9
= 3/1 × 2/3 × 1/9
= 1 × 2 × 1/9
= 2/9
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Help me in these equation9^2 + b^2 = 15.81^2
ANSWER
b = 13
EXPLANATION
We want to solve the equation:
[tex]9^2+b^2=15.81^2[/tex]To do this, simplify the equation:
[tex]81+b^2=249.96[/tex]Isolate b:
[tex]\begin{gathered} b^2=249.96-81 \\ b^2=168.96 \\ Find\text{ the square root of boths side:} \\ b=\sqrt[]{168.96} \\ b=13 \end{gathered}[/tex]That is the answer.
Select all expressions that are squares of linear expressions.ap2 – 6p + 99x2 – 36x2 + 6x + 36Ex+4)2(2d + 8)(2d - 8)x2 + 36
Part a
p2 – 6p + 9
we know that
p2 – 6p + 9=(p-3)^2
so
the given expression is a square of linear equation
Part b
9x2 – 36=(3x-6)(3x+6)
the given expression is not a square of linear equation
Part c
x2 + 6x + 36
the given expression is not a square of linear equation
Part d
(1/2x+4)^2
he given expression is a square of linear equation
PLEASE HELP ME WITH THE QUESTION IN THE PIC BELOW
Let's calculate the distance between F and G:
F=(-4,-2)
G=(2,-2)
[tex]d=\sqrt[]{(2-(-4))^2+(-2-(-2))^2}=\sqrt[]{36}=6[/tex]The distance between M and P is half the distance between F and G, so:
[tex]\frac{d}{2}=3[/tex]The coordinates of P are:
P=(2,-8)
and
M=(x,-8)
So:
[tex]\begin{gathered} 3=\sqrt[]{(x-2)^2+\mleft(-8-\mleft(-8\mright)\mright)^2} \\ 3=x-2 \\ \text{solving for x:} \\ 3+2=x \\ 5=x \\ x=\pm5 \\ \end{gathered}[/tex]Since M is in the 3rd quadrant:
M= (-5,-8)
----------------------------------------------
Let:
(x1,y1)=(-2,1)
(x2,y2)=(-5,4)
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ d=\sqrt[]{(-5-(-2))^2+(4-1)^2} \\ d=\sqrt[]{9+9}=\sqrt[]{18} \end{gathered}[/tex]|2x + 3| < 7?
what’s the solution?
Answer:
Inequality Form: -5<x<2
Interval Notation: (-5,2)
It is stretched horizontally by a factor of 2 and translated up 3 units.
It is compressed horizontally by a factor of 2 and translated up 3 units.
It is stretched vertically by a factor of 2 and translated up 3 units.
It is compressed vertically by a factor of 2 and translated up 3 units.
The correct option B. It is compressed horizontally by a factor of 2 and translated up 3 units.
What is meant by the term translation?The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There isn't any change in the form because it is simply moved from one location to another.For the given question;
The image function is defined as ; y = ㏒(2x) + 3
The parent function is; y = ㏒(x).
The first graph, X, is multiplied by 2 (2x), compressing it horizontally by a factor of 2.The number 3 is then added, which moves the graph up three units.Thus, the image function y = ㏒(2x) + 3 is obtained by the process as,compressed horizontally by a factor of 2 and translated up 3 units.
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The complete question is-
How is the graph of y = ㏒(2x) + 3 related to the graph of y = ㏒(x).
Options are-
A. It is stretched horizontally by a factor of 2 and translated up 3 units.
B. It is compressed horizontally by a factor of 2 and translated up 3 units.
C. It is stretched vertically by a factor of 2 and translated up 3 units.
D. It is compressed vertically by a factor of 2 and translated up 3 units.
The area of a triangle is 40
the length is x+4 and the height is x
what is the value of x
Answer:
16
Step-by-step explanation:
Area of a triangle = 1/2(b×h)
b or l = x+4
h = x
a = 40
1/2(x+4 × x) = 40
1/2(x+4 × x) = 40x + 4 × x / 2 = 40
4 × x = 4x
4x + x = 5x
5x/2 = 40
cross-multiply
40 × 2 = 5x
40 × 2 = 5x80 = 5x
divide both sides by 5
5x/5 = 80/5
5x/5 = 80/5x = 16
Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads East at 25 miles per hour.
Complete an equation for the distance between the friends after t hours.
The equation for the distance between the friends after t hours is 47.17t.
What is the distance between two points?Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
Two companions drive off this way and from a similar spot. One travels North at 40 miles each hour, while different travels East at 25 miles each hour.
The equation for the distance between the friends after t hours is given as,
Let the x-axis as east and the y-axis as north. Then the coordinate after t hours will be (25t, 0) and (0, 40t). Then the distance between them is given as,
D² = (25t - 0)² + (0 - 40t)²
D² = 625t² + 1600t²
D² = 2,225t²
D = 47.17 t
The equation for the distance between the friends after t hours is 47.17t.
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What is the average rate of change of f over the interval [-3, 9]? Give an exact number.
Answer: the answer is -5/6
Step-by-step explanation:
Marie is a college professor. Her annual salary is 66,000. Calculate her monthly taxes belowGross Monthly Income $_____Monthly Federal Income Tax(18.7%) $____Monthly Social Security (FICA (6.2%) $____Monthly Medicare (1.45%) $____Monthly State Tax (4%) $____Monthly local Tax (0.1%) $____Total Monthly Deductions $____Jamals Net Monthly Income $_____
Given
Her annual salary is 66,000.
Procedure
Gross Monthly Income: $66,000/12=$5,500
Monthly Federal Income Tax(18.7%)= $5,500*0.187=$1028.5
Monthly Social Security (FICA (6.2%) =$5,500*0.062=$341
Monthly Medicare (1.45%) =$5,500*0.0145=$79.75
Monthly State Tax (4%)= $5,500*0.04=$220
Monthly local Tax (0.1%)= $5,500*0.001=$5.5
Total Monthly Deductions= $1028.5+$341+$79.75+$220+$5.5=$1,674.75
Jamals Net Monthly Income= $5,500-$1,674.75=$3,825.25
which of the following correctly explains why-14 is an acceptable answer to the equation x2=196?(-14x14=19614*14=196(-14)=196142=196
Daley, this is the solution:
We have: x² = 196
√x² = √196
x = +/- 14
Thus,
• 14 * 14 = 196
,• -14 * -14 = 196
,• 14² = 196
,• -14² = 196
Any of these options could be taken to explain why +/- 14 is an acceptable value for x.
a car can travel 476 miles on 14 gallons of gas write an equation relating to the distance D to the number of gallons G. how many gallons of gas does this car need to travel 578 MI
step 1
Find the unit rate
divide the total miles by the total gallons of gas
so
476/14=34 miles/gal
Let
y ------> the distance in miles
x -----> the number of gal
we have that
the linear equation is equal to
y=34x
part 2
If y=578 miles
Find the value of x
substitute in the equation
578=34x
solve for x
x=578/34
x=17 gallons
How many terms does the following expression have?
5x - 2y +7z-3
Type your answer...
Answer:it has 3 terms
Step-by-step explanation:
the image of the point (-9, 9)under a translation is (-5, 13). find the coordinates of the image of the point (-6, "-7)" under the same translation.
The coordinates of the image of the point (-6, -7) after translation is (-20,-3).
What are coordinates?a pair of figures used to specify a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes. They are typically expressed by the x-value and y-value pair (x,y). Always, the x-coordinate comes before the y-coordinate.
An ordered group of numbers known as coordinates is used to specify a point's location. In the event that the point is on a plane, two numbers are used.
The horizontal and vertical addresses of a point in any two-dimensional (2D) space, such as a sheet of paper or a computer display screen, are called the X and Y coordinates, respectively. These coordinates work as a pair to pinpoint a point's precise location.
A point located at (x,y), translated by (a,b) maps to the point (x+a,y+b).
If we know the location of the point (x,y) and the location of its image (x',y'), we can know the values of (a,b) by subtracting:
(a,b) = (x',y') - (x,y)
We know the coordinates of the point (9,9) and the coordinates of its image (-5,13). Calculate the translation:
(a,b) = (-5,13) - (9,9) = (-14,4)
If the point (-6,-7) is translated under the same conditions, then it will map to the point (-6,-7) + (-14,4) = (-20,-3).
The coordinates of the image are (-20,-3)
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determine the sine and cosine of 90 degrees
Help me please (question in photo)
To graph the ellipse, connect (-2, -3), (6, 2), (14, -3), and (6, -8) with a smooth curve
How to graph an ellipse?The standard form of the equation of an ellipse with center (h, k) and major axis parallel to the x-axis is:
(x-h)²/a² + (y-k)²/b² = 1
When a>b
Major axis length = 2a
Coordinates of the vertices are (h±a, k)
Minor axis length is 2b
Coordinates of covertices are (h, k±b)
Coordinates of foci are (h±c, k). Also c²= a²-b²
Given: the equation (x-6)²/64 + (y+3)²/25 = 1
Comparing the given equation with (x-h)²/a² + (y-k)²/b² = 1:
h = 6, k = -3 => (h, k ) = (6, -3)
Thus, the center of the ellipse is (6, -3)
Coordinates of the vertices are (h±a, k)
Since a² = 64, a = √64 = 8
Thus, the endpoints of the major axis are 8 units from the center
(h±a, k) implies (h-a, k) or (h+a, k). Thus:
(h±a, k) = (6-8, -3) = (-2, -3) or (6+8, -3) = (14, -3)
Coordinates of covertices are (h, k±b)
Since b² = 25, a = √25 = 5
Thus, the endpoints of the minor axis are 5 units from the center
(h, k±b) implies (h, k-b) or (h, k+b). Thus:
(h, k±b) = (6, -3-5) = (6, -8) or (6, -3+5) = (6, 2)
Therefore:
The center of the ellipse is (6, -3). The endpoints of the major axis are 8 units from the center. The endpoints of the minor axis 5 are units from the center.
To graph the ellipse, connect (-2, -3), (6, 2), (14, -3), and (6, -8) with a smooth curve.
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